EXISTENCE OF WEAK SOLUTIONS TO AN ELLIPTIC-PARABOLIC EQUATION WITH VARIABLE ORDER OF NONLINEARITY

摘要

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.