Existence of travelling wave solutions for the heat equation in infinite cylinders with a nonlinear boundary condition

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5 Citations (Scopus)

Abstract

The existence of travelling wave solutions for the heat equation ∂tu-Δu = 0 in an infinite cylinder subject to the nonlinear Neumann boundary condition ∂u/∂n = f(u) is investigated. We show existence of nontrivial solutions for a large class of nonlinearities f. Additionally, the asymptotic behavior at ∞ is studied and regularity properties are established. We use a variational approach in exponentially weighted Sobolev spaces.

Original languageEnglish
Pages (from-to)253-271
Number of pages19
JournalMathematische Nachrichten
Volume281
Issue number2
DOIs
Publication statusPublished - 2008 Feb
Externally publishedYes

Keywords

  • Heat equation
  • Infinite cylinder
  • Nonlinear Neumann boundary condition
  • Travelling wave solution

ASJC Scopus subject areas

  • Mathematics(all)

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