Existence and localization of weak solutions of nonlinear parabolic equations with variable exponent of nonlinearity
This paper deals with a class of nonlinear parabolic equations with Neumann boundary condition. The main feature consists in the presence of the \(p(x,t)\)-Laplace operator, which implies several technical difficulties. By means of the Galerkin approximation technique, the authors establish the existence of weak solutions. Additional qualitative properties of these solutions (extinction in finite time, energy estimates) are also found in the present paper.
scientific article; zbMATH DE number 6174383