Global existence and dynamic structure of solutions for damped wave equation involving the fractional Laplacian

Abstract

We consider strong damped wave equation involving the fractional Laplacian with nonlinear source. The results of global solution under necessary conditions on the critical exponent are established. The existence is proved by using the Galerkin approximations combined with the potential well theory. Moreover, we showed new decay estimates of global solution.

Keywords

• fractional laplacian
• global existence
• fractional sobolev spaces
• potential well
• hyperbolic problem
• 35r11
• 35l20
• 35l70
• 47g20
• 35q91