Asymptotic stability and blow-up of solutions for an edge-degenerate wave equation with singular potentials and several nonlinear source terms of different sign
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Date
2018-01-13
Authors
Jiang, Feida
Luan, Yue
Li, Gang
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We study the initial boundary value problem of an edge-degenerate wave equation. The operator ΔE with edge degeneracy on the boundary ∂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 Ι(u0) > 0. Moreover, we obtain the result of blow-up with initial energy E(0) ≤ d and I(u0) < 0, and give a lower bound for the blow-up time T*.
Description
Keywords
Edge-degenerate, Potential function, Blow-up, Decay, Global solution
Citation
Jiang, F., Luan, Y., & Li, G. (2018). Asymptotic stability and blow-up of solutions for an edge-degenerate wave equation with singular potentials and several nonlinear source terms of different sign. <i>Electronic Journal of Differential Equations, 2018</i>(18), pp. 1-27.