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.
- Heat equation
- Infinite cylinder
- Nonlinear Neumann boundary condition
- Travelling wave solution
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