|
|
| |
| NONLINEAR INITIAL-BOUNDARY VALUE PROBLEM FOR QUASILINEAR HYPERBOLIC SYSTEM |
| |
Citation： |
Li Dening.NONLINEAR INITIAL-BOUNDARY VALUE PROBLEM FOR QUASILINEAR HYPERBOLIC SYSTEM[J].Chinese Annals of Mathematics B,1986,7(2):147~159 |
| Page view： 950
Net amount： 768 |
Authors： |
Li Dening; |
Foundation： |
The result of this paper had ben presented at the seminar of PDE, Mathematics Institute, Fudan University, June, 1983. |
|
|
| Abstract： |
Consider the nonlinear initial-boundary value problem for quasilinear hyperbolic system:
$$\[(*)\left\{ {\begin{array}{*{20}{c}}
{{\partial _t}u = \sum\limits_{j = 1}^n {{A_j}(u){\partial _{{x_i}}}u} + F,in(0,T) \times \Omega ,}\{u(0) = 0,P(u)u{|_{\partial \Omega }} = g.}
\end{array}} \right.\]$$
Let $\[k \ge 2\left[ {\frac{n}{2}} \right] + 6,(F,g) \in {H^k}({B_ + };\Omega ) \times {H^k}({B_ + };\partial \Omega ),\]$, and their traces at $\[t = 0\]$ are zero up to the order $\[k - 1\]$.
If for $\[u = 0\]$, the problem(*) at $\[t = 0\]$ is a Kreiss hyperbolic system, and the boundary conditions satisfy the uniformly Lopatinsky criteria, then there exists a $\[T > 0\]$ such that(*) has a unique $\[{H^2}\]$ solution in $\[(0,T)\]$.
In the Appendix, for symmetric hyperbolic systems, a comparison between the uniformly Lopatinsky condition and the stable admissible condition is given. |
Keywords： |
|
Classification： |
|
|
|
Download PDF Full-Text
|
|
|
|
