ASYMPTOTICAL BEHAVIOR OF A NONLOCAL HYPERBOLIC PROBLEM

Wang Xianchao (P. R. China) and Li Yuxiang (P. R. China)

Received February 3, 2008

Abstract

In this article we consider the asymptotical behavior of a nonlocal hyperbolic problem with decreasing. It is found that the function plays an important role in the asymptotical behavior of the problem, where If then the solution is globally bounded and the steady state is asymptotically stable. If then we discuss the stability of the steady state and prove that the unboundedness of the solution implies finite time blowup if At last we give two examples of

Keywords and phrases: non-local hyperbolic equation, asymptotically behavior, blow-up.