Abstract
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.
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Communicated by LI Ji-bin
Project supported by the National Natural Science Foundation of China (No.10471022) and the Science and Technology Foundation of Ministry of Education of China (Major Projects) (No.104090)
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Shi, Ph., Wang, Mx. Self-similar singular solution of fast diffusion equation with gradient absorption terms. Appl Math Mech 28, 111–118 (2007). https://doi.org/10.1007/s10483-007-0113-1
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DOI: https://doi.org/10.1007/s10483-007-0113-1