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Existence and Uniqueness of Very Singular Solution of a Degenerate Parabolic Equation with Nonlinear Convection

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We here investigate the existence and uniqueness of the nontrivial, nonnegative solutions of a nonlinear ordinary differential equation: satisfying a specific decay rate: with and . Here and . Such a solution arises naturally when we study a very singular self-similar solution for a degenerate parabolic equation with nonlinear convection term defined on the half line .

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Correspondence to ZhongBo Fang.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Equation
  • Parabolic Equation