Note on a higher order pseudo‐parabolic equation with variable exponents

Abstract

In this paper, we study a higher order pseudo‐parabolic equation involving ‐Laplacian with the Navier boundary condition. We use the energy method, the Sobolev embedding inequalities and the Galerkin's approximation to show the classification of singular solutions, including the existence and nonexistence of global, blow‐up, and extinction solutions. Extinction rates and time of extinction solutions, blow‐up time of blow‐up solutions, and decay estimates of global solutions are discussed.