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

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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.

Keywords

Semilinear elliptic equation Cylindrical domain Asymptotic behavior 

Mathematics Subject Classification

35J15 35J25 35J61 
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Notes

Acknowledgments

This work has been performed during a visit of the first author at the Universidad de Chile in Santiago and at the SBAI at the Sapienza Università di Roma. He would like to thank both institutions for their kind hospitality. The second and third authors have been supported by Grants Fondecyt 1130360, 1150066, Fondo Basal CMM and Millenium Nucleus CAPDE NC130017.

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Institute of Applied MathematicsUniversity of ZürichZürichSwitzerland
  2. 2.Departamento de Ingenierıa Matemática and Centro de Modelamiento MatemáticoUniversidad de ChileSantiagoChile

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