|
|
| |
| Global Existence of the Solutions to Nonlinear Hyperbolic Equations in Exterior Domains |
| |
Citation： |
Chen Yunmei,Gao Jianmin.Global Existence of the Solutions to Nonlinear Hyperbolic Equations in Exterior Domains[J].Chinese Annals of Mathematics B,1990,11(3):315~329 |
| Page view： 827
Net amount： 657 |
Authors： |
Chen Yunmei; Gao Jianmin |
|
|
| Abstract： |
This paper deals with the following IBV problem of nonlinear hyperbolic equations
$\[\left\{ {\begin{array}{*{20}{c}}
{{u_{tt}} - \sum\limits_{i,j = 1}^n {{a_{ij}}(u,Du){U_{{x_i}{x_j}}} = b(u,Du),t > 0,x \in \Omega ,} }\{u(0,x) = {u^0}(x),{u_i}(0,x) = {u^1}(v),x \in \Omega ,}\{u(t,x) = 0,t > 0,x \in \partial \Omega ,}
\end{array}} \right.\]$
where Q is the exterior domain of a compact set in R^n, and $|a_{ij}(y)-\delta_{ij}|=0(|y|^k),|b(y)|=0(|y|^{k+1})$, near y=0. It is proved that under suitable assumptions on the smoothness, compatibility conditions and the shape of Q, the above problem has a unique global smooth solution for small initial data, in the case that k=l add n\geq 7 or that k=2 and n\geq 4. Moreover, the solution has some decay properties as t->\infinity. |
Keywords： |
|
Classification： |
|
|
|
Download PDF Full-Text
|
|
|
|
