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

Karol Wroński

doi:10.12775/tmna.2018.010

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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Karol Wroński dr inż.

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License: Copyright (2018 Juliusz Schauder Center for Nonlinear Studies)

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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

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