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<p>Existence theorem for the traveling wave solutions of the “generalized” nonlinear reaction-diffusion equation <InlineEquation ID="IEq1"><EquationSource Format="TEX">\(u_{t}=(u^{m})_{xx}+f(u),\)</EquationSource></InlineEquation> is established for any <InlineEquation ID="IEq2"><EquationSource Format="TEX">\(m&gt;1.\)</EquationSource></InlineEquation> This form generalizes the classical linear form with <InlineEquation ID="IEq3"><EquationSource Format="TEX">\(m=1.\)</EquationSource></InlineEquation> A critical value of the minimum wave speed <InlineEquation ID="IEq4"><EquationSource Format="TEX">\(c^{*}\)</EquationSource></InlineEquation> is obtained as <InlineEquation ID="IEq5"><EquationSource Format="TEX">\(c^{*}=2m\sqrt{f^{\prime }(0)}\)</EquationSource></InlineEquation>, which extends the results obtained by Fisher, Kolmogorov, and others.</p>

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Generalized Reaction-Diffusion Equation With Density Dependent Diffusion

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月29日

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  • Lazhar Bougoffa,
  • Ammar Khanfer

摘要

Existence theorem for the traveling wave solutions of the “generalized” nonlinear reaction-diffusion equation \(u_{t}=(u^{m})_{xx}+f(u),\) is established for any \(m>1.\) This form generalizes the classical linear form with \(m=1.\) A critical value of the minimum wave speed \(c^{*}\) is obtained as \(c^{*}=2m\sqrt{f^{\prime }(0)}\), which extends the results obtained by Fisher, Kolmogorov, and others.