Global stability of traveling wave solutions of generalized Korteveg-de Vries-Burgers equation with non-constant dissipation parameter
Shargatov, V. A. 1Chugainova, A. P. 1Kolomiytsev, G., V1
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作者信息
1. Russian Acad Sci
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Abstract
We consider traveling wave solutions of generalized Korteweg-de Vries-Burgers equation when the flux function has two inflection points. The dissipation coefficient mu depends only on the spatial coordinate in some moving coordinate system and increases monotonically from mu(1) to mu(2) in the narrow spatial region. Some external influence causes the change in the dissipation coefficient. The set of admissible shocks is defined. In order to determine which discontinuities are admissible, we study the nonlinear (global) stability of traveling wave solutions. Scenarios of the evolution of linearly unstable traveling waves are described, and asymptotics of unstable solutions are found. We find that a stable traveling wave solution and a solution with a time-dependent structure can correspond to the same admissible shock. (c) 2022 Elsevier B.V. All rights reserved.
NSTL
Elsevier