A singular non-Newton filtration equation with logarithmic nonlinearity: global existence and blow-up

Abstract

In this paper, we study the initial-boundary value problem of the singular non-Newton filtration equation with logarithmic nonlinearity. By using the concavity method, we obtain the existence of finite time blow-up solutions at initial energy $J(u_0) \leqslant d$. Furthermore, we discuss the asymptotic behavior of the weak solution and prove that the weak solution converges to the corresponding stationary solution as $t\rightarrow +\infty $. Finally, we give sufficient conditions for global existence and blow-up of solutions at initial energy $J(u_0)>d$.

Keywords

• Logarithmic nonlinearity
• Non-Newton filtration equation
• Singular potential
• Global existence
• Blow-up
• Logarithmic nonlinearity