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We study decay properties of the solution to the 1d damped wave equation in the Fujita subcritical case \(p<3\) . Namely, we consider appropriate small initial data, such that global solution exists even for \(p<3\) and obtain an estimate of the \(L^\infty \) norm that gives a decay faster than the classical linear time decay \(t^{-1/2}\) . We assume initial data in space of type \(L^1 \cap L^\infty \) or corresponding Sobolev spaces without imposing some additional space dependent weights in these spaces.

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Decay of Solution to 1d Subcritical Damped Wave Equation Under Some Initial Condition

  • 会议论文

  • 发表日期：

    2025年

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  • Kazumasa Fujiwara,
  • Vladimir Simeonov Georgiev

摘要

We study decay properties of the solution to the 1d damped wave equation in the Fujita subcritical case \(p<3\) . Namely, we consider appropriate small initial data, such that global solution exists even for \(p<3\) and obtain an estimate of the \(L^\infty \) norm that gives a decay faster than the classical linear time decay \(t^{-1/2}\) . We assume initial data in space of type \(L^1 \cap L^\infty \) or corresponding Sobolev spaces without imposing some additional space dependent weights in these spaces.