On the behavior of positive solutions of semilinear elliptic equations in asymptotically cylindrical domains

Michel Chipot; Juan Dávila; Manuel del Pino

doi:10.1007/s11784-016-0349-1

On the behavior of positive solutions of semilinear elliptic equations in asymptotically cylindrical domains

Michel Chipot, Juan Dávila, Manuel del Pino

Department of Mathematical Sciences

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Abstract

The goal of this note is to study the asymptotic behavior of positive solutions for a class of semilinear elliptic equations which can be realized as minimizers of their energy functionals. This class includes the Fisher-KPP and Allen–Cahn nonlinearities. We consider the asymptotic behavior in domains becoming infinite in some directions. We are in particular able to establish an exponential rate of convergence for this kind of problems.

Original language	English
Pages (from-to)	205-213
Number of pages	9
Journal	Journal of Fixed Point Theory and Applications
Volume	19
Issue number	1
Early online date	4 Nov 2016
DOIs	https://doi.org/10.1007/s11784-016-0349-1
Publication status	Published - 1 Mar 2017

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Cite this

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abstract = "The goal of this note is to study the asymptotic behavior of positive solutions for a class of semilinear elliptic equations which can be realized as minimizers of their energy functionals. This class includes the Fisher-KPP and Allen–Cahn nonlinearities. We consider the asymptotic behavior in domains becoming infinite in some directions. We are in particular able to establish an exponential rate of convergence for this kind of problems.",

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AU - del Pino, Manuel

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N2 - The goal of this note is to study the asymptotic behavior of positive solutions for a class of semilinear elliptic equations which can be realized as minimizers of their energy functionals. This class includes the Fisher-KPP and Allen–Cahn nonlinearities. We consider the asymptotic behavior in domains becoming infinite in some directions. We are in particular able to establish an exponential rate of convergence for this kind of problems.

AB - The goal of this note is to study the asymptotic behavior of positive solutions for a class of semilinear elliptic equations which can be realized as minimizers of their energy functionals. This class includes the Fisher-KPP and Allen–Cahn nonlinearities. We consider the asymptotic behavior in domains becoming infinite in some directions. We are in particular able to establish an exponential rate of convergence for this kind of problems.

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DO - 10.1007/s11784-016-0349-1

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JO - Journal of Fixed Point Theory and Applications

JF - Journal of Fixed Point Theory and Applications

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ER -

On the behavior of positive solutions of semilinear elliptic equations in asymptotically cylindrical domains

Abstract

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