Existence of Weak Solutions to an Elliptic-Parabolic Equation with Variable Order of Nonlinearity

详细

We consider an equation with variable nonlinearity of the form |u|^p(x), in which the parabolic term can vanish, i.e., in the corresponding domain the parabolic equation becomes “elliptic.” Under the weak monotonicity conditions (nonstrict inequality) we prove the existence of a solution to the first mixed problem in a cylinder with a bounded base.