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<p>We consider the <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13_2025_2162_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(L^{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>-boundedness of the solution of the Cauchy problem for a wave equation with time-dependent wave speeds. We treat it in the one-dimensional Euclidean space <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13_2025_2162_Article_IEq5.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\textbf{R}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="bold">R</mi> </math></EquationSource> </InlineEquation>. We adopt a simple multiplier method by using a special property of the one dimensional space.</p>

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\(L^2\)-boundedness for 1-D wave equations with time variable coefficients

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  • 发表日期：

    2025年8月8日

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  • Ryo Ikehata

摘要

We consider the \(L^{2}\) L 2 -boundedness of the solution of the Cauchy problem for a wave equation with time-dependent wave speeds. We treat it in the one-dimensional Euclidean space \(\textbf{R}\) R . We adopt a simple multiplier method by using a special property of the one dimensional space.