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Zlatoš, Andrej

Generalized traveling waves in disordered media: existence, uniqueness, and stability. (English) Zbl 1270.35173

Arch. Ration. Mech. Anal. 208, No. 2, 447-480 (2013).
Summary: 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 of solutions with exponentially decaying initial data to time translations 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.

Cited in 44 Documents

MSC:

35C07 Traveling wave solutions
35K57 Reaction-diffusion equations
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
35B35 Stability in context of PDEs

Keywords:

inhomogeneous ignition reactions; exponentially decaying initial data; reaction-advection-diffusion equations
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References:

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