Self-Similar Singular Solution of Fast Diffusion Equation With Gradient Absorption Terms

SHI Pei-hu; WANG Ming-xin

Volume 28 Issue 1

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SHI Pei-hu, WANG Ming-xin. Self-Similar Singular Solution of Fast Diffusion Equation With Gradient Absorption Terms[J]. Applied Mathematics and Mechanics, 2007, 28(1): 99-106.

Citation:

SHI Pei-hu, WANG Ming-xin. Self-Similar Singular Solution of Fast Diffusion Equation With Gradient Absorption Terms[J]. Applied Mathematics and Mechanics, 2007, 28(1): 99-106.

Citation:

SHI Pei-hu, WANG Ming-xin. Self-Similar Singular Solution of Fast Diffusion Equation With Gradient Absorption Terms[J]. Applied Mathematics and Mechanics, 2007, 28(1): 99-106.

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Self-Similar Singular Solution of Fast Diffusion Equation With Gradient Absorption Terms

Department of Mathematics, Southeast University, Nanjing 210096, P. R. China

Received Date: 2004-05-28
Rev Recd Date: 2006-10-09
Publish Date: 2007-01-15

Abstract

Abstract

The self-similar singular solution of the fast diffusion equation with nonlinear gradient absorption terms had been studied. By a self-similar transformation, the self-similar solutions satisfy a boundary value problem of nonlinear ODE. Using the shooting arguments, the existence and uniqueness of the solution to the initial data problem of the nonlinear ODE had been investigated, 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 the investigation of the classification of the solutions. In case of existence, the self-similar singular solution is very singular solution.
- fast diffusion equation,
- gradient absorption,
- self-similar singular solution,
- very singular solution

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References

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