On a singular parabolic p-Laplacian equation with logarithmic nonlinearity

Abstract

In this paper, we considered a singular parabolic -Laplacian equation with logarithmic nonlinearity in a bounded domain with homogeneous Dirichlet boundary conditions. We established the local solvability by the technique of cut-off combining with the method of Faedo-Galerkin approximation. Based on the potential well method and Hardy-Sobolev inequality, the global existence of solutions was derived. In addition, we obtained the results of the decay. The blow-up phenomenon of solutions with different indicator ranges was also given. Moreover, we discussed the blow-up of solutions with arbitrary initial energy and the conditions of extinction.

Keywords

• non-newton filtration equation
• singular potential
• logarithmic nonlinearity
• global existence
• decay
• blow-up