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| EXISTENCE AND NONEXISTENCE OF GLOBAL SOLUTION OF NONLINEAR PARABOLIC EQUATION WITH NONLINEAR BOUNDARY CONDITION |
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Citation： |
Wu Yonghui,Wang Mingxin.EXISTENCE AND NONEXISTENCE OF GLOBAL SOLUTION OF NONLINEAR PARABOLIC EQUATION WITH NONLINEAR BOUNDARY CONDITION[J].Chinese Annals of Mathematics B,1995,16(3):371~378 |
| Page view： 1236
Net amount： 792 |
Authors： |
Wu Yonghui; Wang Mingxin |
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| Abstract： |
This paper deals with the existence and nonexistence of global positive
solution of the following equation:
$$ \cases u_t=\nabla(u^{q-1}\nabla u)- \a u^m, \qquad & x\in \o, \ \ t>0,\\dfrac {\partial u}{\partial n} =u^p, &x\in \p\o, \ t>0,\u(x, 0)=u_0(x)>0, &x\in \bar\o,\endcases$$
where $p, q, m, \a$ are parameters with $q\ge 1, \ m, p >0, \a\ge 0. \ \o\subset
R^N$ is a
bounded domain with $\p\o$ smooth enough, $ N\ge 1.$ The
necessary and sufficient
conditions for the global existence of solution are obtained. |
Keywords： |
Nonlinear parabolic equiation, Nonlinear boundary condition,
Existence,Blow-up, Subsolution and supersolution |
Classification： |
35K60 |
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