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Article overview
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Blow-up of a structural acoustics model | | Baowei Feng
; Yanqiu Guo
; Mohammad A. Rammaha
; | | Date: |
1 Jan 2023 | | Abstract: | This article studies the finite time blow-up of weak solutions to a
structural acoustics model consisting of a semilinear wave equation defined on
a bounded domain $Omegasubsetmathbb{R}^3$ which is strongly coupled with a
Berger plate equation acting on the elastic wall, namely, a flat portion of the
boundary. The system is influenced by several competing forces, including
boundary and interior source and damping terms. We stress that the power-type
source term acting on the wave equation is allowed to have a supercritical
exponent, in the sense that its associated Nemytskii operators is not locally
Lipschitz from $H^1$ into $L^2$. In this paper, we prove the blow-up results
for weak solutions when the source terms are stronger than damping terms, by
considering two scenarios of the initial data: (i) the initial total energy is
negative; (ii) the initial total energy is positive but small, while the
initial quadratic energy is sufficiently large. The most significant challenge
in this work arises from the coupling of the wave and plate equations on the
elastic wall. | | Source: | arXiv, 2301.00485 | | Services: | Forum | Review | PDF | Favorites | |
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