Existence and nonexistence of global solutions for doubly nonlinear diffusion equations with logarithmic nonlinearity

Abstract

In this paper, we study an initial-boundary value problem for a doubly nonlinear diffusion equation with logarithmic nonlinearity. By using the potential well method, we give some threshold results on existence or nonexistence of global weak solutions in the case of initial data with energy less than or equal to potential well depth. In addition, the asymptotic behavior of solutions is also discussed.

Keywords

• global existence
• blow-up
• asymptotic behavior
• logarithmic nonlinearity