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Heteroclinic solutions of Allen-Cahn type equations with a general elliptic operator

Abstract

We consider a generalization of the Allen-Cahn type equation in divergence form $-\rm{div}(\nabla G(\nabla u(x,y)))+F_u(x,y,u(x,y))=0$. This is more general than the usual Laplace operator. We prove the existence and regularity of heteroclinic solutions under standard ellipticity and $m$-growth conditions.

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Copyright (2018 Juliusz Schauder Center for Nonlinear Studies)

Details

Category:
Articles
Type:
artykuł w czasopiśmie wyróżnionym w JCR
Published in:
Topological Methods in Nonlinear Analysis no. 52, pages 729 - 738,
ISSN: 1230-3429
Language:
English
Publication year:
2018
Bibliographic description:
Wroński K.: Heteroclinic solutions of Allen-Cahn type equations with a general elliptic operator// Topological Methods in Nonlinear Analysis. -Vol. 52, nr. 2 (2018), s.729-738
DOI:
Digital Object Identifier (open in new tab) 10.12775/tmna.2018.010
Verified by:
Gdańsk University of Technology

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