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].

Keywords:

• fourth-order nonlinear wave equation
• viscous damping
• global existence
• nonexistence
• potential well

AMS Subject Classifications::

• 35L05
• 76A10

Acknowledgements

This work was supported by the National Natural Science Foundation of China (11101102), PhD Programs Foundation of Ministry of Education of China (20102304120022), the Support Plan for the Young College Academic Backbone of Heilongjiang Province (1252G020), the Natural Science Foundation of Heilongjiang Province (A201014), Foundational Science Foundation of Harbin Engineering University and Fundamental Research Funds for the Central Universities (HEUCF20111101).