刊名:Journal of Mathematical Analysis and Applications
出版年:2017
出版时间:15 February 2017
年:2017
卷:446
期:2
页码:1255-1273
全文大小:408 K
文摘
In this paper, we consider the initial-boundary value problem for a generalized Kelvin–Voight equation with p-Laplacian and a damping term:
Here is the velocity field, P(x,t) is the pressure, ν is the viscosity kinematic coefficient, and ϰ is the viscosity relaxation coefficient (is a length scale parameter characterizing the elasticity of the fluid). The coefficient γ and the exponents p, m are given constants. Under appropriate conditions on the data, we prove the existence and uniqueness of the global and local weak solutions. Under several assumptions on the exponents p, m, the coefficients ν, ϰ, and specified initial data, a finite time blow-up and the behavior of the solutions for large times are also established.