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

✍ Scribed by Mads Kyed

• Publisher: John Wiley and Sons
• Year: 2008
• Tongue: English
• Weight: 234 KB
• Volume: 281
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.200710599

✦ Synopsis

Abstract

The existence of travelling wave solutions for the heat equation ∂~t~ u –Δ__u__ = 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. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)