Travelling wave solutions of the heat equation in an unbounded cylinder with a non-linear boundary condition

Let $Omega$ be a bounded domain in R². The existence of travelling wave solutions for the heat equation in the unbounded cylinder $RimesOmega$ subject to the nonlinear boundary condition $partial u over partial n = f(u)$ is investigated. Finding such a solution amounts to solving the elliptic PDE Delta u - c partial_x u = 0 for $(x,y)inRimesOmega$ with $partial u over partial n = f(u)$ on $RimespartialOmega$. The main result is the existence of a non-trivial solution of this equation for a large class of non-linearities $f$. Additionally, asymptotic behavior at $x=pminfty$ and regularity properties are established. A variational approach is used. More specifically, a weak solution is found as the minimizer of a constrained minimization problem posed in a weighted Sobolev space. Due to underlying domain $RimesOmega$ being unbounded, this problem suffers from a lack of compactness. The problem is solved using a suitable approximation.

Grantor dc:publisher

Publikationsserver der RWTH Aachen University

Year dc:date

2005

Author dc:creator

• Kyed, Mads

Contributors dc:contributor

• Lugscheider, Erich

• info:eu-repo/classification/ddc/510
• Wärmeleitungsgleichung
• nichtlineares Randwertproblem
• fortschreitende Wellenlösung
• Mathematik
• semilinear parabolic equations
• semilinear elliptic equations
• cylindrical domains
• nonlinear boundary condition
• travelling wave

Statement dc:rights

• info:eu-repo/semantics/openAccess

Language dc:language

eng

Identifier

https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-121673%22

OAI identifier oai:identifier

oai:publications.rwth-aachen.de:59933