Feida Jiang, Yue Luan, Gang Li
Abstract:
We study the initial boundary value problem of an edge-degenerate wave equation.
The operator
with edge degeneracy on the boundary
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
and
.
Moreover, we obtain the result of blow-up with initial energy
and
,
and give a lower bound for the blow-up time
.
Submitted May 12, 2017. Published January 13, 2018.
Math Subject Classifications: 35L20, 35L80, 33B44.
Key Words: Edge-degenerate; potential function; blow-up; decay; global solution.
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Feida Jiang College of Mathematics and Statistics Nanjing University of Information Science and Technology Nanjing 210044, China email: jfd2001@163.com |
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Yue Luan College of Mathematics and Statistics Nanjing University of Information Science and Technology Nanjing 210044, China email: yluan_sunflower@163.com |
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Gang Li College of Mathematics and Statistics Nanjing University of Information Science and Technology Nanjing 210044, China email: ligang@nuist.edu.cn |
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