EXISTENCE AND NONEXISTENCE OF GLOBAL SOLUTIONS OF THE INITIAL-BOUNDARY VALUE PROBLEM FOR SOME DEGENERATE HYPERBOLIC EQUATION

摘要

The author considers the global existence and global nonexistence of the initial-boundary value problem for some degenerate hyperbolic equation of the form u_(tt) - div(|▽u|~(p-2)▽u) = |u|~mu, (x,t) ∈ [0,+∞) x Ω with p > 2 and m > 0. He deals with the global solutions by D.H.Sattinger's potential well ideas. At the same time, when the initial energy is positive, but appropriately bounded, the global nonexistence of solutions is verified by using the analysis method.