Asymptotic stability and blow-up of solutions for an edge-degenerate wave equation with singular potentials and several nonlinear source terms of different sign
We study the initial boundary value problem of an edge-degenerate wave equation. The operator $\Delta_{\mathbb{E}}$ with edge degeneracy on the boundary $\partial E$ was investigated in the literature. We give the invariant sets and the vacuum isolating behavior of solutions by introducing a fami...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2018-01-01
|
| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2018/18/abstr.html |
| Summary: | We study the initial boundary value problem of an edge-degenerate wave equation.
The operator $\Delta_{\mathbb{E}}$ with edge degeneracy on the boundary
$\partial E$ 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 $E(0)\leq d$ and $I(u_0)>0$.
Moreover, we obtain the result of blow-up with initial energy $E(0)\leq d$
and $I(u_0)<0$, and give a lower bound for the blow-up time $T^*$. |
|---|---|
| ISSN: | 1072-6691 |