scholarly journals Fujita type theorem for a class of coupled quasilinear convection–diffusion equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yanan Zhou ◽  
Yan Leng ◽  
Yuanyuan Nie
Keyword(s):  
Critical Case ◽  
Large Time ◽  
Blow Up ◽  
Type Theorem ◽  
Large Time Behavior ◽  
Diffusion Equations ◽  
Time Behavior ◽  
Convection Term ◽  
Diffusion Term ◽  
Convection Diffusion

AbstractIn this paper, we establish the Fujita type theorem for a homogeneous Neumann outer problem of the coupled quasilinear convection–diffusion equations and formulate the critical Fujita exponent. Besides, the influence of diffusion term, reaction term, and convection term on the global existence and the blow-up property of the problem is revealed. Finally, we discuss the large time behavior of the solution to the outer problem in the critical case and describe the asymptotic behavior of the solution.

scholarly journals Large Time Behavior of Nonlinear Finite Volume Schemes for Convection-Diffusion Equations

2020 ◽  
Vol 58 (5) ◽  
pp. 2544-2571
Author(s):  
Clément Cancès ◽  
Claire Chainais-Hillairet ◽  
Maxime Herda ◽  
Stella Krell
Keyword(s):  
Finite Volume ◽  
Large Time ◽  
Large Time Behavior ◽  
Diffusion Equations ◽  
Time Behavior ◽  
Finite Volume Schemes ◽  
Convection Diffusion

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

2021 ◽  
Vol 121 (2) ◽  
pp. 125-157
Author(s):  
S. Antontsev ◽  
H.B. de Oliveira ◽  
Kh. Khompysh
Keyword(s):  
Boundary Value Problem ◽  
Unique Solvability ◽  
Anisotropic Diffusion ◽  
Large Time ◽  
Blow Up ◽  
Large Time Behavior ◽  
Time Behavior ◽  
Diffusion Relaxation ◽  
Global And Local ◽  
Problem Data

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.

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