Qualitative properties for a pseudo-parabolic equation with nonlocal reaction term

Abstract

Abstract This paper deals with the qualitative properties of solutions for null Neumann initial boundary value problem to a nonlocal pseudo-parabolic equation in the sense of H1(Ω) $H^{1}(\varOmega )$-norm. We establish sufficient conditions to guarantee that the solution with initial energy exists globally or blows up at finite time under an appropriate range of parameters. Moreover, life span of the blow-up solution, decay rate of the global solution, and growth estimate are derived.

Keywords

• Pseudo-parabolic equation
• Nonlocal reaction term
• Blow-up
• Life span
• Asymptotic behavior