Initial boundary value problem for a class of fourth-order wave equation with viscous damping term

Abstract

In this article we study the initial boundary value problem for a class of fourth-order nonlinear wave equation with viscous damping term u tt − αu xxt + u xxxx = f(u x ) x . By argument related to the potential well-convexity method, we prove the global existence and nonexistence of the solution. Further, we give some sharp conditions for global existence and nonexistence of the solution. This generalizes the results obtained in Chen and Lu [G. Chen and B. Lu, The initial-boundary value problems for a class of nonlinear wave equations with damping term, J. Math. Anal. Appl. 351 (2009), pp. 1–15].