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

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Abstract

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 (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Keywords

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