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| PROPERTIES OF THE BOUNDARY FLUX OF A SINGULAR DIFFUSION PROCESS |
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Citation： |
YIN Jingxue,WANG Chunpeng.PROPERTIES OF THE BOUNDARY FLUX OF A SINGULAR DIFFUSION PROCESS[J].Chinese Annals of Mathematics B,2004,25(2):175~182 |
| Page view： 1338
Net amount： 745 |
Authors： |
YIN Jingxue; WANG Chunpeng |
Foundation： |
Project supported by the 973 Project of the Ministry of Science and Technology of China, the Outstanding
Youth Foundation of China (No.10125107) and the Department of Mathematics of Jilin University. |
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| Abstract： |
The authors study the singular diffusion equation
$$
\quad\frac{\partial u}{\partial t} =\hbox{div}(\rho^\alpha|\nabla
u|^{p-2}\nabla u), \qquad (x,t)\in Q_T=\Omega\times(0,T),
$$
where $\Omega\subset\mathbb R^n$ is a bounded domain with
appropriately smooth boundary $\partial\Omega$,
$\rho(x)=\hbox{dist}(x,\partial\Omega)$, and prove that if
$\alpha\ge p-1$, the equation admits a unique solution subject
only to a given initial datum without any boundary value
condition, while if $0<\alpha |
Keywords： |
Boundary flux, Singular diffusion, Boundary degeneracy |
Classification： |
35K65, 35K55 |
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