Existence results for nonlinear pseudoparabolic problems

In this paper, we are interested in nonlinear pseudoparabolic problems of type: f(t,x,∂tu)−Div[a(x,u,∂tu)∇u]−Div[b(x,u,∂tu)∇∂ut]=g.ff is a nondecreasing continuous function with respect to its third argument, aa is bounded and bb is positive and bounded.The result of existence is proved thanks to a time discretization scheme. Then, we derive some applications to the equation of Barenblatt, a degenerate case and differential inclusions. Finally, some numerical illustrations are proposed.