Existence results for nonlinear pseudoparabolic problems

Abstract

In this paper, we are interested in nonlinear pseudoparabolic problems of type: f ( t , x , ∂ t u ) − Div [ a ( x , u , ∂ t u ) ∇ u ] − Div [ b ( x , u , ∂ t u ) ∇ ∂ u t ] = g . f is a nondecreasing continuous function with respect to its third argument, a is bounded and b 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.