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Search results for: UNBOUNDED DOMAINS
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Numerical approximations of parabolic functional differential equations on unbounded domains
PublicationSkonstruowano schematy różnicowe zagadnień początkowych dla nieliniowych parabolicznych równań różniczkowo funkcyjnych. Przedstawiono twierdzenie o oszacowaniu błędu rozwiązań przybliżonych dla równań różnicowo funkcyjnych typu Volterry z niewiadomą funkcją kilku zmiennych. Udowodniono twierdzenie o zbieżności jawnych schematów różnicowych. Podano przykłady numeryczne.
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The saga of a fish: from a survival guide to closing lemmas
PublicationIn 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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A Framework for Searching in Graphs in the Presence of Errors
PublicationWe consider a problem of searching for an unknown target vertex t in a (possibly edge-weighted) graph. Each vertex-query points to a vertex v and the response either admits that v is the target or provides any neighbor s of v that lies on a shortest path from v to t. This model has been introduced for trees by Onak and Parys [FOCS 2006] and for general graphs by Emamjomeh-Zadeh et al. [STOC 2016]. In the latter, the authors provide...
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A Generalized Version of the Lions-Type Lemma
PublicationIn this short paper, I recall the history of dealing with the lack of compactness of a sequence in the case of an unbounded domain and prove the vanishing Lions-type result for a sequence of Lebesgue-measurable functions. This lemma generalizes some results for a class of Orlicz–Sobolev spaces. What matters here is the behavior of the integral, not the space