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

Mads Kyed

doi:10.1002/mana.200710599

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

Mads Kyed^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	253-271
Number of pages	19
Journal	Mathematische Nachrichten
Volume	281
Issue number	2
DOIs	https://doi.org/10.1002/mana.200710599
Publication status	Published - 2008 Feb
Externally published	Yes

Keywords

Heat equation
Infinite cylinder
Nonlinear Neumann boundary condition
Travelling wave solution

ASJC Scopus subject areas

Mathematics(all)

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10.1002/mana.200710599

Cite this

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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.",

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AB - 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.

KW - Heat equation

KW - Infinite cylinder

KW - Nonlinear Neumann boundary condition

KW - Travelling wave solution

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

Abstract

Keywords

ASJC Scopus subject areas

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