Stabilization of the Moving Front Solution of the Reaction-Diffusion-Advection Problemстатья
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Дата последнего поиска статьи во внешних источниках: 26 июня 2024 г.
Аннотация:We consider the initial-boundary value problem of reaction-diffusion-advection that hasa solution of a front form. The statement comes from the theory of wave physics. We study thequestion of the solution stabilizing to the stationary one. Proof of the stabilization theorem is basedon the concepts of upper and lower solutions and corollaries from comparison theorems. The upperand lower solutions with large gradients are constructed as modifications of the formal movingfront asymptotic approximation in a small parameter. The main idea of the proof is to show that theupper and lower solutions of the initial-boundary value problem get into the attraction domain of theasymptotically stable stationary solution on a sufficiently large time interval. The study conducted inthis work gives an answer about the non-local attraction domain of the stationary solution and cangive some stationing criteria. The results are illustrated by computational examples.