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<p>We investigate a nonlinear shallow water wave equation, which contains the Fornberg–Whitham model. The <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13661_2025_2018_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>2</mn> </msup> </math></EquationSource> <EquationSource Format="TEX">$L^{2}$</EquationSource> </InlineEquation> conservation law of solutions for the nonlinear equation is derived. Employing the Riccati-type differential inequalities, we give sufficient conditions such that the wave breaking of solutions happens at finite time. The wave-breaking rate and lifespan of solutions are also discussed.</p>

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Blow-up phenomena for a nonlinear shallow water wave model

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年2月24日

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  • Siyu Wei,
  • Jun Meng,
  • Jun Ma,
  • Shaoyong Lai

摘要

We investigate a nonlinear shallow water wave equation, which contains the Fornberg–Whitham model. The L 2 $L^{2}$ conservation law of solutions for the nonlinear equation is derived. Employing the Riccati-type differential inequalities, we give sufficient conditions such that the wave breaking of solutions happens at finite time. The wave-breaking rate and lifespan of solutions are also discussed.