Initial-boundary value problem for a fourth-order plate equation with Hardy-Hénon potential and polynomial nonlinearity

Xu Liu; Jun Zhou; Xu Liu; Jun Zhou

doi:10.3934/era.2020032

Electronic Research Archive

2020, Volume 28, Issue 2: 599-625. doi: 10.3934/era.2020032

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Initial-boundary value problem for a fourth-order plate equation with Hardy-Hénon potential and polynomial nonlinearity

Xu Liu ,
Jun Zhou ^,

School of Mathematics and Statistics, Southwest University, Chongqing 400715, China

Received: 01 March 2020 Revised: 01 March 2020
35G10, 35B40

In this paper, the initial-boundary value problem for a fourth-order plate equation with Hardy-Hénon potential and polynomial nonlinearity is invsitgated. First, we establish the local well-posedness of solutions by means of the semigroup theory. Then by using ordinary differential inequalities, potential well theory and energy estimate, we study the conditions on global existence and finite time blow-up. Moreover, the lifespan (i.e., the upper bound of the blow-up time) of the finite time blow-up solution is estimated.
- Fourth-order plate equation,
- Hardy-Hénon potential,
- finite time blow-up,
- global existence,
- lifespan
Citation: Xu Liu, Jun Zhou. Initial-boundary value problem for a fourth-order plate equation with Hardy-Hénon potential and polynomial nonlinearity[J]. Electronic Research Archive, 2020, 28(2): 599-625. doi: 10.3934/era.2020032

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Abstract

In this paper, the initial-boundary value problem for a fourth-order plate equation with Hardy-Hénon potential and polynomial nonlinearity is invsitgated. First, we establish the local well-posedness of solutions by means of the semigroup theory. Then by using ordinary differential inequalities, potential well theory and energy estimate, we study the conditions on global existence and finite time blow-up. Moreover, the lifespan (i.e., the upper bound of the blow-up time) of the finite time blow-up solution is estimated.

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