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| On the Uniqueness Solutions of Nonlinear Degenerate Parabolic Equations(in English) |
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Citation： |
Dong Guangchang,Ye Qixiao.On the Uniqueness Solutions of Nonlinear Degenerate Parabolic Equations(in English)[J].Chinese Annals of Mathematics B,1982,3(3):279~284 |
| Page view： 822
Net amount： 925 |
Authors： |
Dong Guangchang; Ye Qixiao |
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| Abstract： |
本文证明，在条件$a(s)>0(s>0),a(0)=0,b(s)=O(a(s)^\lambda)(s \geq 0,0 \leq \lambda \geq 1/2),s^\mu=O(a(s))(s \geq 0, \mu >0$之下，混合问题
${u_t} = {(a(u){u_x})_x} + b(u){u_x},(x,t) \in R = \{ (x,t)| - 1 < x < 1,0 < t < T\} $
$u(x,0)=u_0(x)(\geq0),-1 \leqx \leq 1$
$u(-1,0)=\psi_1(t)(\geq0),u(1,t)=\psi _w(t)(\geq 0),0 \leq t \leq T$
当$\mu<1,\lambda \geq0$或$\mu \geq1,2\lambda+1/ \mu>1$时，解为唯一的，这改善了[1,2]的结果。 |
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