A family of potential wells for a wave equation

Yang Liu; Wenke Li; Yang Liu; Wenke Li

doi:10.3934/era.2020041

Electronic Research Archive

2020, Volume 28, Issue 2: 807-820. doi: 10.3934/era.2020041

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A family of potential wells for a wave equation

Yang Liu ^{1
,},
Wenke Li ^{2
,
,}

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

Received: 01 March 2020 Revised: 01 April 2020
Primary: 35L05, 35A01, 35B44

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.
- Wave equations,
- global existence,
- blow-up,
- potential wells
Citation: Yang Liu, Wenke Li. A family of potential wells for a wave equation[J]. Electronic Research Archive, 2020, 28(2): 807-820. doi: 10.3934/era.2020041

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Abstract

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.

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