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| INVARIANT SETS AND THE HUKUHARA-KNESER PROPERTY FOR PARABOLIC SYSTEMS |
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Citation： |
Yan Ziqian.INVARIANT SETS AND THE HUKUHARA-KNESER PROPERTY FOR PARABOLIC SYSTEMS[J].Chinese Annals of Mathematics B,1984,5(1):119~132 |
| Page view： 761
Net amount： 724 |
Authors： |
Yan Ziqian; |
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| Abstract： |
In this paper we are concerned with the nonlinear boundary value problem for parabolic system
$$\[\left\{ {\begin{array}{*{20}{c}}
{Lu = f(x,t,u,Du),x \in \Omega ,0 < t \le T,}\{Bu = g(x,t,u),x \in \partial \Omega ,0 \le t \le T,}\{u(x,0) = h(x),x \in \bar \Omega }
\end{array}\begin{array}{*{20}{c}}
{}&{(1)}
\end{array}} \right.\]$$
where $\[Lu = ({L_1}{u_1}, \cdots ,{L_N}{u_N})\]$ with $\[{L_k}\]$ the second order uniformly parabolic operators which may be different from one another, and $\[Bu = ({B_1}{u_1}, \cdots ,{B_N}{u_N})\]$ wther the Dirichlet
boundary operators or the regular oblique derivative ones. We have proved that a certain form of convex set is invariant for (1), that there exist solutions to (1) if $\[f = f(x,t,u,p)\]$ has an almost quadratic growth in p, and that the set of solutions possesses the Hukuhara-
Kneser property. |
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