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<p>The initial boundary value problem of a class of coupled hyperbolic systems with logarithmic source terms is considered. In this article, we classify the initial data for the global existence, finite time blow-up and long time decay of the solution. By using potential well method combined with Sobolev embedding theorem, the sufficient initial conditions of global existence, asymptotic behavior, the upper and lower bounds of blow-up time are derived at low energy level <i>E</i>(0) &lt; <i>d</i>. These results are extended in parallel to the critical case <i>E</i>(0) = <i>d</i>. Besides, with additional assumptions on initial data, the finite time blow up result is given with arbitrary positive initial energy <i>E</i>(0) &gt; 0.</p>

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Global Existence and Blow up for Hyperbolic Coupled Systems with Internal Damping and Logarithmic Nonlinearities

  • 期刊论文

  • 发表日期：

    2025年5月29日

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  • Yi-fei Dai,
  • Zhi-fei Zhang

摘要

The initial boundary value problem of a class of coupled hyperbolic systems with logarithmic source terms is considered. In this article, we classify the initial data for the global existence, finite time blow-up and long time decay of the solution. By using potential well method combined with Sobolev embedding theorem, the sufficient initial conditions of global existence, asymptotic behavior, the upper and lower bounds of blow-up time are derived at low energy level E(0) < d. These results are extended in parallel to the critical case E(0) = d. Besides, with additional assumptions on initial data, the finite time blow up result is given with arbitrary positive initial energy E(0) > 0.