A variational approach to travelling waves
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Submission date: 15. Nov. 2001
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It is proven, that a single semilinear parabolic equation in an unbounded cylinder with cubic-like source or boundary flux admit travelling waves. The problem is reformulated as a constrained minimization problem, where the wave velocity is related to the infimum. This characterization implies the monotone dependence of the velocity on the domain, the nonlinearity and the boundary conditions. Using rearrangement of the minimizer the monotonicity of the wave profile is proven.