ASYMPTOTIC STABILITY AND BLOW-UP OF SOLUTIONS FOR AN EDGE-DEGENERATE WAVE EQUATION WITH SINGULAR POTENTIALS AND SEVERAL NONLINEAR SOURCE TERMS OF DIFFERENT SIGN

作者：Jiang, Feida^*; Luan, Yue; Li, Gang

来源：Electronic Journal of Differential Equations, 2018, 18.

• Edge -degenerate
• potential function
• blow-up
• decay
• global solution

We study the initial boundary value problem of an edge-degenerate wave equation. The operator Delta(E) with edge degeneracy on the boundary partial derivative E was investigated in the literature. We give the invariant sets and the vacuum isolating behavior of solutions by introducing a family of potential wells. We prove that the solution is global in time and exponentially decays when the initial energy satisfies E(0) <= d and I((u)) > 0. Moreover, we obtain the result of blow-up with initial energy E(0) <= d and I(u(0)) < 0, and give a lower bound for the blow-up time T*.

• 出版日期2018-1-13
• 单位南京信息工程大学