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| Existence and Uniqueness of Weak Solutions of Uniformly Degenerate Quasilinear Parabolic Equations |
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Citation： |
Chen Yazhe.Existence and Uniqueness of Weak Solutions of Uniformly Degenerate Quasilinear Parabolic Equations[J].Chinese Annals of Mathematics B,1985,6(2):131~146 |
| Page view： 1043
Net amount： 778 |
Authors： |
Chen Yazhe; |
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| Abstract： |
In this paper we deal with the quasilinear parabolic equation
$[\frac{{\partial u}}{{\partial t}} = \frac{\partial }{{\partial {x_i}}}[{a_{ij}}(x,t,u)\frac{{\partial u}}{{\partial {x_j}}}] + {b_i}(x,t,u)\frac{{\partial u}}{{\partial {x_i}}} + c(x,t,u)\]$
which is uniformly degenerate at u=0. Under some assumptions we prove existence and uniqueness of nonnegative weak solutions to the Cauchy problem and the first boundary value problem for this equation. Furthermore, the weak solutions are globally Holder continuous. |
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