BLOW-UP OF SOLUTION FOR A VISCOELASTIC WAVE EQUATION WITH DELAY

doi:10.1007/s10473-019-0124-7

摘要/Abstract

摘要： In this paper, we consider the following viscoelastic wave equation with delay
|u_t|^ρ u_tt-△u-△u_tt + ƒ₀^t g(t - s)△u(s)ds + μ₁u_t(x, t) + μ₂u_t(x, t - τ)=b|u|^p-2 u
in a bounded domain. Under appropriate conditions on μ₁, μ₂, the kernel function g, the nonlinear source and the initial data, there are solutions that blow up in finite time.

关键词: blow up, nonlinear source, wave equation, delay, viscoelastic

Abstract: In this paper, we consider the following viscoelastic wave equation with delay
|u_t|^ρ u_tt-△u-△u_tt + ƒ₀^t g(t - s)△u(s)ds + μ₁u_t(x, t) + μ₂u_t(x, t - τ)=b|u|^p-2 u
in a bounded domain. Under appropriate conditions on μ₁, μ₂, the kernel function g, the nonlinear source and the initial data, there are solutions that blow up in finite time.

Key words: blow up, nonlinear source, wave equation, delay, viscoelastic

吴舜堂. BLOW-UP OF SOLUTION FOR A VISCOELASTIC WAVE EQUATION WITH DELAY[J]. 数学物理学报(英文版), 2019, 39(1): 329-338.

Shun-Tang WU. BLOW-UP OF SOLUTION FOR A VISCOELASTIC WAVE EQUATION WITH DELAY[J]. Acta mathematica scientia,Series B, 2019, 39(1): 329-338.

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