Generalized Traveling Waves in Disordered Media: Existence, Uniqueness, and Stability

Details Generalized Traveling Waves in Disordered Media: Existence, Uniqueness, and Stability Generalized Traveling Waves in Disordered Media: Existence, Uniqueness, and Stability

2009-01-15

arxiv.org/abs/0901.2369v1

Mathematics

Analysis of PDEs

Scientific paper

We prove existence, uniqueness, and stability of transition fronts (generalized traveling waves) for reaction-diffusion equations in cylindrical domains with general inhomogeneous ignition reactions. We also show uniform convergence of solutions with exponentially decaying initial data to time translates of the front. In the case of stationary ergodic reactions the fronts are proved to propagate with a deterministic positive speed. Our results extend to reaction-advection-diffusion equations with periodic advection and diffusion.

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