Kelvin-Voigt equations with anisotropic diffusion, relaxation and damping: Blow-up and large time behavior

Antontsev S. De Oliveira H.B. Khompysh K.
2021 IOS Press BV

Asymptotic Analysis
2021 #121 Issue 2 125 - 157 pp.

A nonlinear initial and boundary-value problem for the Kelvin-Voigt equations with anisotropic diffusion, relaxation and absorption/damping terms is considered in this work. The global and local unique solvability of the problem was established in (J. Math. Anal. Appl. 473(2) (2019) 1122-1154). In the present work, we show how all the anisotropic exponents of nonlinearity and all anisotropic coefficients should interact with the problem data for the solutions of this problem display exponential and polynomial time-decays. We also establish the conditions for the solutions of this problem to blow-up in a finite time in three different cases: problem without convection, full anisotropic problem, and the problem with isotropic relaxation.

anisotropic damping , anisotropic diffusion , anisotropic relaxation , blow-up , Kelvin-Voigt equations , large time behavior

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CMAFCIO, Universidade de Lisboa, Portugal
Lavrentyev Institute of Hydrodynamics SB RAS, Novosibirsk, Russian Federation
FCT, Universidade Do Algarve, Portugal
Al-Farabi Kazakh National University, Kazakhstan

CMAFCIO
Lavrentyev Institute of Hydrodynamics SB RAS
FCT
Al-Farabi Kazakh National University

10 лет помогаем публиковать статьи Международный издатель

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