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Wyniki wyszukiwania dla: DIFFERENTIAL EQUATION
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Monotone iterative method to second order differential equations with deviating arguments involving Stieltjes integral boundary conditions
PublikacjaWe use a monotone iterative method for second order differential equations with deviating arguments and boundary conditions involving Stieltjes integrals. We establish sufficient conditions which guarantee that such problems have extremal solutions in the corresponding region bounded by lower and upper solutions. We also discuss the situation when problems have coupled quasi-solutions. We illustrate our results by three examples.
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Solving Boundary Value Problems for Second Order Singularly Perturbed Delay Differential Equations by ε-Approximate Fixed-Point Method
PublikacjaIn this paper, the boundary value problem for second order singularly perturbed delay differential equation is reduced to a fixed-point problem v = Av with a properly chosen (generally nonlinear) operator A. The unknown fixed-point v is approximated by cubic spline vh defined by its values vi = vh(ti) at grid points ti, i = 0, 1, ... ,N. The necessary for construction the cubic spline and missing the first derivatives at the boundary...
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Positive solutions of one-dimensional p-Laplacian boundary value problems for fourth-order differential equations with deviating arguments
PublikacjaPraca dotyczy istnienia dodatnich rozwiązań dla równań różniczkowych rzędu czwartego z warunkami brzegowymi z odchylonymi argumentami. Stosując twierdzenie o punkcie stałym dla stożków podano warunki dostateczne na istnienia takich rozwiązań.
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Nonnegative solutions to nonlocal boundary value problems for systems of second-order differential equations dependent on the first-order derivatives
PublikacjaStosując tw. Avery-Petersona o punkcie stałym, podano warunki dostateczne na istnienie nieujemnych rozwiązań dla układów równań różniczkowych rzędu drugiego z argumentami opóźnionymi i wyprzedzonymi oraz warunkami brzegowymi zawierającymi całki Stieltjesa. Praca zawiera wiele przykładów.
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Infinite systems of hyperbolic functional differential equations. Ukr.Mat. Zurn.*2003 t. 55 nr 12 s. 1678-1696 bibliogr. 21 poz. Nieskończone układy hiperboliczne równań różniczkowo-funkcyjnych.
PublikacjaWykazano istnienie prawie klasycznego rozwiązania zagadnienia Cauchy´ego.Dowód wykorzystuje metodę bicharakterystyk i nierówności całkowo-funkcyjne.
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Structural Stability of Nonautonomous Systems
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Chaos in vibroimpact systems with one degree of freedom in a neighborhood of chatter generation: II
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A Criterion for Conditional Instability by the First Approximation for Solutions of Differential Systems
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Chaos in vibroimpact systems with one degree of freedom in a neighborhood of chatter generation: I
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Different types of solvability conditions for differential operators
PublikacjaSolvability conditions for linear differential equations are usually formulated in terms of orthogonality of the right-hand side to solutions of the homogeneous adjoint equation. However, if the corresponding operator does not satisfy the Fredholm property such solvability conditions may be not applicable. For this case, we obtain another type of solvability conditions, for ordinary differential equations on the real axis, and...
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Straightened characteristics of McKendrick-von Foerster equation
PublikacjaWe study the McKendrick-von Foerster equation with renewal (that is the age-structured model, with total population dependent coefficient and nonlinearity). By using a change of variables, the model is then transformed to a standard age-structured model in which the total population dependent coefficient of the transport term reduces to a constant 1. We use this transformation to get existence, uniqueness of solutions of the problem...
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Fixed point indices of iterated smooth maps in arbitrary dimension
PublikacjaWe give a complete description of possible sequences ofindices of iterations of f at an isolated fixed point, answering inaffirmative the Chow, Mallet-Paret and Yorke conjecture posed in[S.N. Chow, J. Mallet-Parret, J.A. Yorke, A periodic point index whichis a bifurcation invariant, in: Geometric Dynamics, Rio de Janeiro,1981, in: Lecture Notes in Math., vol. 1007, Springer, Berlin, 1983,pp. 109-131].
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Implicit difference methods for first order partial differential functional equations
PublikacjaKlasyczne rozwiązania problemów początkowo brzegowych przybliżane są rozwiązaniami uwikłanych metod różnicowych. Wykazana została zbieżność i stabilność uwikłanych schematów. Dowód stabilności opiera się na technice porównawczej z nieliniowym oszacowaniem typu Perrona dla funkcji danych.
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Heteroclinic solutions for a class of the second order Hamiltonian systems
PublikacjaW pracy dowodzi się istnienia rozwiązań heteroklicznicznych dla pewnej klasy równań różniczkowych zwyczajnych drugiego rzędu typu hamiltonowskiego.
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The cohomological span of LS-Conley index
PublikacjaIn this paper we introduce a new homotopy invariant – the cohomological span of LS-Conley index. We prove the theorems on the existence of critical points for a class of strongly indefinite functionals with the gradient of the form Lx+K(x), where L is bounded linear and K is completely continuous. We give examples of Hamiltonian systems for which our methods give better results than the Morse inequalities. We also give a formula...
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Homotopy invariance of the Conley index and local Morse homology in Hilbert spaces
PublikacjaIn this paper we introduce a new compactness condition — Property-(C) — for flows in (not necessary locally compact) metric spaces. For such flows a Conley type theory can be developed. For example (regular) index pairs always exist for Property-(C) flows and a Conley index can be defined. An important class of flows satisfying the this compactness condition are LS-flows. We apply E-cohomology to index pairs of LS-flows and obtain...
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Integrate-and-fire models with an almost periodic input function
PublikacjaWe investigate leaky integrate-and-fire models (LIF models for short) driven by Stepanov and μ-almost periodic functions. Special attention is paid to the properties of the firing map and its displacement, which give information about the spiking behavior of the considered system. We provide conditions under which such maps are well-defined and are uniformly continuous. We show that the LIF models with Stepanov almost periodic...
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The saga of a fish: from a survival guide to closing lemmas
PublikacjaIn the paper by D. Burago, S. Ivanov and A. Novikov, “A survival guide for feeble fish”, it has been shown that a fish with limited velocity can reach any point in the (possibly unbounded) ocean provided that the fluid velocity field is incompressible, bounded and has vanishing mean drift. This result extends some known global controllability theorems though being substantially nonconstructive. We give a fish a different recipe...
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Homoclinic solutions for a class of the second order Hamiltonian systems
PublikacjaW niniejszej pracy badamy istnienie orbit homoklinicznych dlaukładu Hamiltonowskiego drugiego rzędu: q^{..} + V_{q}(t,q) = f(t), gdzie V z iloczynu kartezjańskiego R x R^{n} do R jest postaciV(t,q) = -K(t,q) + W(t,q). Zakładamy, ze V jest T-okresowe ze względuna zmienną t, K spełnia tzw. ''pinching'' warunek, W jest superliniowew nieskończoności, a norma f w L^{2} jest wystarczająco mała.Orbitę homokliniczną takiego układu znajdujemy...
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A Strategy to Locate Fixed Points and Global Perturbations of ODE’s: Mixing Topology with Metric Conditions
PublikacjaIn this paper we discuss a topological treatment for the planar system z' = f (t, z) + g(t, z) where f and g are T -periodic in time and g(t, z) is bounded. Namely, we study the effect of g(t, z) in two different frameworks: isochronous centers and time periodic systems having subharmonics. The main tool employed in the proofs consists of a topological strategy to locate fixed points in the class of orientation preserving embedding...
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Local fixed point indices of iterations of planar maps
PublikacjaW artykule podana zostaje postać indeksów iteracji dla pewnej klasy odwzorowań planarnych. Podstawowymi narzędziami stosowanym w pracy są liczba Nielsena i indeks Conleya.
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On the Existence of Homoclinic Type Solutions of a Class of Inhomogenous Second Order Hamiltonian Systems
PublikacjaWe show the existence of homoclinic type solutions of a class of inhomogenous second order Hamiltonian systems, where a C1-smooth potential satisfies a relaxed superquadratic growth condition, its gradient is bounded in the time variable, and a forcing term is sufficiently small in the space of square integrable functions. The idea of our proof is to approximate the original system by time-periodic ones, with larger and larger...
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Description of the solution set of the von Karman equations for a circular plate in a small neighbourhood of a simple bifurcation point
PublikacjaW niniejszej pracy badamy równania von Karmana dla cienkiej, sprężystej, kołowej płyty na sprężystym podłożu, poddawanej działaniu sił ściskających wzdłuż brzegu. Są to równania różniczkowe cząstkowe IV rzędu. Stosując metody analizy nieliniowej, opisujemy zbiór rozwiązań równań von Karmana w małym otoczeniu jednokrotnego punktu bifurkacji.Badania były finansowane przez grant nr 1 P03A 042 29.
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The Palais–Smale condition for the Hamiltonian action on a mixed regularity space of loops in cotangent bundles and applications
PublikacjaWe show that the Hamiltonian action satisfies the Palais-Smale condition over a “mixed regular- ity” space of loops in cotangent bundles, namely the space of loops with regularity H^s, s ∈ (1/2, 1), in the baseand H^{1−s} in the fiber direction. As an application, we give a simplified proof of a theorem of Hofer-Viterbo on the existence of closed characteristic leaves for certain contact type hypersufaces in cotangent bundles.
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Homoclinics for singular strong force Lagrangian systems in R^N
PublikacjaWe will be concerned with the existence of homoclinics for second order Hamiltonian systems in R^N (N>2) given by Hamiltonians of the form H(t,q,p)=Φ(p)+V(t,q), where Φ is a G-function in the sense of Trudinger, V is C^2-smooth, periodic in the time variable, has a single well of infinite depth at a point ξ and a unique strict global maximum 0 at the origin. Under a strong force type condition aroud the singular point ξ, we prove...
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A note on the Morse homology for a class of functionals in Banach spaces involving the 2p-area functional
PublikacjaIn this paper we show how to construct Morse homology for an explicit class of functionals involving the 2p-area functional. The natural domain of definition of such functionals is the Banach space W_0^{1,2p}(\Omega), where p > n/2 and \Omega \subet R^n is a bounded domain with sufficiently smooth boundary. As W_0^{1,2p}(\Omega) is not isomorphic to its dual space,critical points of such functionals cannot be non-degenerate...
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On the Fenchel–Moreau conjugate of G-function and the second derivative of the modular in anisotropic Orlicz spaces
PublikacjaIn this paper, we investigate the properties of the Fenchel–Moreau conjugate of G-function with respect to the coupling function c(x, A) = |A[x]2 |. We provide conditions that guarantee that the conjugate is also a G-function. We also show that if a G-function G is twice differentiable and its second derivative belongs to the Orlicz space generated by the Fenchel–Moreau conjugate of G then the modular generated by G is twice differentiable...
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Existence and uniqueness for neutral equations with state dependent delays
PublikacjaW pracy w celu wykazania istnienia i jednoznaczności rozwiązania równania została zaprezentowana metoda porównawcza.
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A solution of non-linear differential problem with application to selected geotechnical problems
PublikacjaA certain non-linear differential equation containing a power of unknown function being the solution is considered with application to selected geotechnical problems. The equation can be derived to a linear differential equation by a proper substitution and properties of the operations G and S.
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Computational issues of solving the 1D steady gradually varied flow equation
PublikacjaIn this paper a problem of multiple solutions of steady gradually varied flow equation in the form of the ordinary differential energy equation is discussed from the viewpoint of its numerical solution. Using the Lipschitz theorem dealing with the uniqueness of solution of an initial value problem for the ordinary differential equation it was shown that the steady gradually varied flow equation can have more than one solution....
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Estimation of a Stochastic Burgers' Equation Using an Ensemble Kalman Filter
PublikacjaIn this work, we consider a difficult problem of state estimation of nonlinear stochastic partial differential equations (SPDE) based on uncertain measurements. The presented solution uses the method of lines (MoL), which allows us to discretize a stochastic partial differential equation in a spatial dimension and represent it as a system of coupled continuous-time ordinary stochastic differential equations (SDE). For such a system...
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On the convergence of a finite-difference discretization à la Mickens of the generalized Burgers–Huxley equation
PublikacjaIn this note, we establish the property of convergence for a finite-difference discretization of a diffusive partial differential equation with generalized Burgers convective law and generalized Hodgkin–Huxley reaction. The numerical method was previously investigated in the literature and, amongst other features of interest, it is a fast and nonlinear technique that is capable of preserving positivity, boundedness and monotonicity....
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Inverse Flood Routing Using Simplified Flow Equations
PublikacjaThe paper considers the problem of inverse flood routing in reservoir operation strategy. The aim of the work is to investigate the possibility of determining the hydrograph at the upstream end based on the hydrograph required at the downstream end using simplified open channel flow models. To accomplish this, the linear kinematic wave equation, the diffusive wave equation and the linear Muskingum equation are considered. To achieve...
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Crystallization kinetics study of dynamically vulcanized PA6/NBR/HNTs nanocomposites by nonisothermal differential scanning calorimetry
PublikacjaInvestigation of crystallization behavior and kinetics of thermoplastic elastomer nanocomposites was the subject of limited works because of complexities associated with semiexperimental modeling of such phenomenon in a system containing components having completely different behavior in the molten state. Nonisothermal crystallization kinetics of dynamically vulcanized PA6/NBR/HNTs thermoplastic elastomer nanocomposites was mathematically...
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Discussion of “Development of an Accurate Time integration Technique for the Assessment of Q-Based versus h-Based Formulations of the Diffusion Wave Equation for Flow Routing” by K. Hasanvand, M.R. Hashemi and M.J. Abedini
PublikacjaThe discusser read the original with great interest. It seems, however, that some aspects of the original paper need additional comments. The authors of the original paper discuss the accuracy of a numerical solution of the diffusion wave equation formulated with respect to different state variables. The analysis focuses on nonlinear equations in the form of a single transport equation with the discharge Q (volumetric flow rate)...
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Comparison of Average Energy Slope Estimation Formulas for One-dimensional Steady Gradually Varied Flow
PublikacjaTo find the steady flow water surface profile, it is possible to use Bernoulli’s equation, which is a discrete form of the differential energy equation. Such an approach requires the average energy slope between cross-sections to be estimated. In the literature, many methods are proposed for estimating the average energy slope in this case, such as the arithmetic mean, resulting in the standard step method, the harmonic mean and...
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PROPERTIES OF ONE DIMENSIONAL OPEN-CHANNEL STEADY FLOW EQUATIONS
PublikacjaIn this paper properties of discrete forms of one dimensional steady gradually varied flow equations are discussed. Such forms of flow equations are obtained as a result of approximation of their differential forms, which is required to solve them numerically. For such purpose explicit or implicit numerical approximation schemes for ordinary differential equations can be applied. It turns out that dependently on the chosen approximation...
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Existence and uniqueness of monotone and bounded solutions for a finite-difference discretization a` la Mickens of the generalized Burgers–Huxley equation.
PublikacjaDeparting from a generalized Burgers–Huxley partial differential equation, we provide a Mickens-type, nonlinear, finite-difference discretization of this model. The continuous system is a nonlinear regime for which the existence of travelling-wave solutions has been established previously in the literature. We prove that the method proposed also preserves many of the relevant characteristics of these solutions, such as the positivity,...
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On local buckling of cold-formed channel members
PublikacjaThe paper deals with local buckling of the compressed flanges of cold-formed thin-walled channel beams subjected to pure bending or axially compressed columns. Arbitrarily shaped flanges of open cross-sections and the web-flange interactions are taken into account. Buckling deformation of a beam flange is described by displacement related to torsion of the flange about the line of its connection with the web. Total potential energy...
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Torsional buckling and post-buckling of columns made of aluminium alloy
PublikacjaThe paper concerns torsional buckling and the initial post-buckling of axially compressed thin-walled aluminium alloy columns with bisymmetrical cross-section. It is assumed that the column material behaviour is described by the Ramberg–Osgood constitutive equation in non-linear elastic range. The stationary total energy principle is used to derive the governing non-linear differential equation. An approximate solution of the equation...
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Application of muscle model to the musculoskeletal modeling
PublikacjaThe purpose of this paper is to investigate new fusiform muscle models. Each of these models treats a muscle as a system composedof parts characterized by different mechanical properties. These models explain the influence of differences in the stiffness of lateral parts and the degree of muscle model discretization. Each muscle model is described by a system of differential equations and a single integro-differential equation....
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Significant Production of Thermal Energy in Partially Ionized Hyperbolic Tangent Material Based on Ternary Hybrid Nanomaterials
PublikacjaNanoparticles are frequently used to enhance the thermal performance of numerous materials. This study has many practical applications for activities that have to minimize losses of energy due to several impacts. This study investigates the inclusion of ternary hybrid nanoparticles in a partially ionized hyperbolic tangent liquid passed over a stretched melting surface. The fluid motion equation is presented by considering the...
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The finite difference methods of computation of X-rays propagation through a system of many lenses
PublikacjaThe propagation of X-ray waves through an optical system consisting of many beryllium X-ray refrac- tive lenses is considered. In order to calculate the propagation of electromagnetic in the optical sys- tem, two differential equations are considered. First equation for an electric field of a monochromatic wave and the second equation derived for complex phase of the same electric The propagation of X-ray waves through an optical system...
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On forced vibrations of piezo-flexomagnetic nano-actuator beams
PublikacjaThe effect of excitation frequency on the piezomagnetic Euler-Bernoulli nanobeam taking the flexomagnetic material phenomenon into consideration is investigated in this chapter. The magnetization with strain gradients creates flexomagneticity. We couple simultaneously the piezomagnetic and flexomagnetic properties in an inverse magnetization. Resemble the flexoelectricity, the flexomagneticity is also size-dependent. So, it has...
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Flexomagnetic response of buckled piezomagnetic composite nanoplates
PublikacjaIn this paper, the equation governing the buckling of a magnetic composite plate under the influence of an in-plane one-dimensional magnetic field, assuming the concept of flexomagnetic and considering the resulting flexural force and moment, is investigated for the first time by different analytical boundary conditions. To determine the equation governing the stability of the plate, the nonlocal strain gradient theory has been...
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Discrete and continuous fractional persistence problems – the positivity property and applications
PublikacjaIn this article, we study the continuous and discrete fractional persistence problem which looks for the persistence of properties of a given classical (α=1) differential equation in the fractional case (here using fractional Caputo’s derivatives) and the numerical scheme which are associated (here with discrete Grünwald–Letnikov derivatives). Our main concerns are positivity, order preserving ,equilibrium points and stability...
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Elastic distortional buckling of thin-walled bars of closed quadratic cross-section
PublikacjaIn this study a thin-walled bar with closed quadratic cross-section is considered. The elastic stability of axially compressed bar related to the cross-section distortion is investigated. The governing differential equation is derived with aid of the principle of stationary total potential energy. The critical load for the simply supported bar is found in analytical form and it is compared with the FEM solution. Sufficient accuracy...
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Green function diagonal for a class of heat equations
PublikacjaA construction of the heat kernel diagonal is considered as element of generalized zeta function theory, which gradient at the origin defines determinant of a differential operator in a technique for regularizing quadratic path integral. Some classes of explicit expressions of the Green function in the case of finite-gap potential coefficient of the heat equation are constructed. An algorithm and program for Mathematica are presented...
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Acoustic heating produced in the boundary layer
Publikacja: Instantaneous acoustic heating of a viscous fluid flow in a boundary layer is the subject of investigation. The governing equation of acoustic heating is derived by means of a special linear combination of conservation equations in the differential form, which reduces all acoustic terms in the linear part of the final equation but preserves terms belonging to the thermal mode. The procedure of decomposition is valid in a weakly...
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Verification of algorithms determining wave loads on support structure of wind turbine
PublikacjaThe offshore wind turbines require determination of wave loads on their support structure. This structure is fixed and, therefore, this problem is reduced to solving only the diffraction problem, which is determined by Laplace equation and conditions on the following boundaries: on the support structure, on the sea free surface and on its bottom, and at infinity on free surface. The linear problem was applied to determine the wave...