# American Institute of Mathematical Sciences

June  2020, 28(2): 807-820. doi: 10.3934/era.2020041

## A family of potential wells for a wave equation

 1 College of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730124, China 2 College of Power and Energy Engineering, Harbin Engineering University, Harbin, Heilongjiang 150001, China

* Corresponding author: Wenke Li, liwenke@hrbeu.edu.cn

Received  March 2020 Revised  April 2020 Published  May 2020

In this paper, a family of potential wells are introduced by means of the modified depths of the potential wells. These potential wells are employed to study the initial-boundary value problem for a wave equation. The expression of the depths of the potential wells is derived. Global existence and finite time blow-up of weak solutions with the subcritical initial energy and the critical initial energy are obtained, respectively. Moreover, some numerical simulations of the depths of the potential wells are carried out.

Citation: Yang Liu, Wenke Li. A family of potential wells for a wave equation. Electronic Research Archive, 2020, 28 (2) : 807-820. doi: 10.3934/era.2020041
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##### References:
$d(\delta)\thicksim\delta$; $p = 3$, $C_1 = 2$
$d(0.5)\thicksim C_1, p$
$d(\delta)\thicksim\delta, p$; $C_1 = 2$
$g_1(y)\thicksim y_\delta$
$y_{1}\thicksim d(1), p$
$y_{0.5}\thicksim C_1, p$
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