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We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
A variational approach to travelling waves
Steffen HeinzeAbstract
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.
- Received:
- 15.11.01
- Published:
- 15.11.01