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

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