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.
