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In this note, we study the Cauchy problem of the semilinear damped wave equation and our aim is the small data global existence for noncompactly supported initial data. For this problem, Ikehata and Tanizawa [5] introduced the energy method with the exponential-type weight function \(e^{|x|^2/(1+t)}\) , which is the so-called Ikehata–Todorova–Yordanov type weight. In this paper, we suggest another weight function of the form \((1+|x|^2/(1+t))^{\lambda }\) , which allows us to treat polynomially decaying initial data and give a simpler proof than the previous studies treating such initial data.

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Revisit on Global Existence of Solutions for Semilinear Damped Wave Equations in \(\mathbb {R}^N\) with Noncompactly Supported Initial Data

  • 会议论文

  • 发表日期：

    2025年

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  • Yuta Wakasugi

摘要

In this note, we study the Cauchy problem of the semilinear damped wave equation and our aim is the small data global existence for noncompactly supported initial data. For this problem, Ikehata and Tanizawa [5] introduced the energy method with the exponential-type weight function \(e^{|x|^2/(1+t)}\) , which is the so-called Ikehata–Todorova–Yordanov type weight. In this paper, we suggest another weight function of the form \((1+|x|^2/(1+t))^{\lambda }\) , which allows us to treat polynomially decaying initial data and give a simpler proof than the previous studies treating such initial data.