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 initialboundary value problem for a wave equation. The expression of the depths of the potential wells is derived. Global existence and finite time blowup 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[J]. Electronic Research Archive, 2020, 28(2): 807820. doi: 10.3934/era.2020041
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 initialboundary value problem for a wave equation. The expression of the depths of the potential wells is derived. Global existence and finite time blowup 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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