GLOBAL SOLUTION AND BLOW-UP OF LOGARITHMIC KLEIN-GORDON EQUATION

摘要

The initial-boundary value problem for a class of semilinear Klein-Gordon equation with logarithmic nonlinearity in bounded domain is studied. The existence of global solution for this problem is proved by using potential well method, and obtain the exponential decay of global solution through introducing an appropriate Lyapunov function. Meanwhile, the blow-up of solution in the unstable set is also obtained.