Self-similar singular solution of fast diffusion equation with gradient absorption terms

  • Shi Pei-hu  (石佩虎)Email author
  • Wang Ming-xin  (王明新)


The self-similar singular solution of the fast diffusion equation with nonlinear gradient absorption terms are studied. By a self-similar transformation, the self-similar solutions satisfy a boundary value problem of nonlinear ordinary differential equation (ODE). Using the shooting arguments, the existence and uniqueness of the solution to the initial data problem of the nonlinear ODE are investigated, and the solutions are classified by the region of the initial data. The necessary and sufficient condition for the existence and uniqueness of self-similar very singular solutions is obtained by investigation of the classification of the solutions. In case of existence, the self-similar singular solution is very singular solution.

Key words

fast diffusion equation gradient absorption self-similar singular solution very singular solution 

Chinese Library Classification


2000 Mathematics Subject Classification

35K15 35K65 


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Copyright information

© Editorial Committee of Appl. Math. Mech. 2007

Authors and Affiliations

  • Shi Pei-hu  (石佩虎)
    • 1
    Email author
  • Wang Ming-xin  (王明新)
    • 1
  1. 1.Department of MathematicsSoutheast UniversityNanjingP. R. China

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