Study of the solutions to a model porous medium equation with variable exponent of nonlinearity

The authors of this paper study the Dirichlet problem of the following equationut−div(|u|ν(x,t)∇u)=f−|u|p(x,t)−1u.ut−div(|u|ν(x,t)∇u)=f−|u|p(x,t)−1u. The existence and uniqueness of weak solutions are proven. Also, the properties of the solutions are studied which include the property of finite speed of propagation of disturbances, localization property and the property of vanishing at a finite time etc.