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Global Nonexistence for A Viscoelastic Wave Equation with Acoustic Boundary Conditions

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Abstract

This paper deals with a class of nonlinear viscoelastic wave equation with dam** and source terms

${u_{tt}} - \Delta u - \Delta {u_t} - \Delta {u_{tt}} + \int_0^t {g(t - s)\Delta u(s)ds + {u_t}{u_t}{^{m - 2}} = u|u|{^{p - 2}}} $

with acoustic boundary conditions. Under some appropriate assumption on relaxation function g and the initial data, we prove that the solution blows up in finite time if the positive initial energy satisfies a suitable condition.

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Authors and Affiliations

  1. School of Science, Dalian Jiaotong University, Dalian, 116028, China

    Jiali Yu

  2. School of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, China

    Jiali Yu, Yadong Shang & Huafei Di

Authors
  1. Jiali Yu
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  2. Yadong Shang
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  3. Huafei Di
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Corresponding author

Correspondence to Yadong Shang.

Additional information

This work was supported by the NSF of China (11626070, 11801108), the Scientific Program of Guangdong Provience (2016A030310262), the College Scientific Research Project of Guangzhou City (1201630180), the Program for the Innovation Research Grant for the Postgraduates of Guangzhou University (2017GDJC-D08).

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Yu, J., Shang, Y. & Di, H. Global Nonexistence for A Viscoelastic Wave Equation with Acoustic Boundary Conditions. Acta Math Sci 40, 155–169 (2020). https://doi.org/10.1007/s10473-020-0111-2

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  • DOI: https://doi.org/10.1007/s10473-020-0111-2

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