Global and blow-up solutions for a quasilinear hyperbolic equation with strong damping

作者：Sun, Fuqin^*; Wang, Mingxin; Li, Huiling

来源：Nonlinear Analysis-Theory Methods & Applications, 2010, 73(5): 1408-1425.

DOI：10.1016/j.na.2010.05.001

• Hyperbolic equation
• Strong damping
• Global solutions
• Blow-up
• Decay estimates

In this paper, we study a quasilinear hyperbolic equation with strong damping. Firstly, by use of the successive approximation method and a series of classical estimates, we prove the local existence and uniqueness of a weak solution. Secondly, via some inequalities, the potential method and the concave method, we derive the asymptotic and blow-up behavior of the weak solution with different conditions.

• 出版日期2010-9-1
• 单位东南大学; 天津职业技术师范大学