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

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

Journal

Asymptotic Analysis
ISSN: 0921-7134

Output data

Year: 2021, Volume: 121, Number: 2, Pages: 125-157 Pages count : 33 DOI: 10.3233/asy-201597

Tags

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

Authors

Antontsev S. ^1,2 , de Oliveira H.B. ^1,3 , Khompysh Kh. ⁴

Affiliations

1	CMAFCIO, Universidade de Lisboa, Portugal
2	Lavrentyev Institute of Hydrodynamics SB RAS, Novosibirsk, Russia.
3	FCT, Universidade Do Algarve, Portugal
4	Al-Farabi Kazakh National University, Kazakhstan

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.

Antontsev S. , de Oliveira H.B. , Khompysh K.
Kelvin–Voigt equations with anisotropic diffusion, relaxation and damping: Blow-up and large time behavior
Asymptotic Analysis. 2021. V.121. N2. P.125-157. DOI: 10.3233/asy-201597 WOS Scopus РИНЦ OpenAlex

Web of science:	WOS:000607781600002
Scopus:	2-s2.0-85099365996
Elibrary:	45010319
OpenAlex:	W2999605720

DB	Citing
Scopus	9
OpenAlex	8
Elibrary	6
Web of science	9