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| A NECESSARY AND SUFFICIENT CONDITION OF EXISTENCE OF GLOBAL SOLUTIONS FOR SOME NONLINEAR HYPERBOLIC EQUATIONS |
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Citation： |
Zhang Quande.A NECESSARY AND SUFFICIENT CONDITION OF EXISTENCE OF GLOBAL SOLUTIONS FOR SOME NONLINEAR HYPERBOLIC EQUATIONS[J].Chinese Annals of Mathematics B,1995,16(4):461~468 |
| Page view： 1014
Net amount： 781 |
Authors： |
Zhang Quande; |
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| Abstract： |
The author considers the Klien--Gordon equations $ u_{tt}
-\Delta u+\mu u=f(u)~~(\mu>0,~|f(u)|\leq c|u|^{\alpha +1})$. The
necessary and sufficient condition of existence of global solutions is obtained for $ E(0)=
\frac {1}{2}(\|u_1\|_{L^2}^2 + \| \nabla u_0\|_{L^2}^2 +\mu \|u_0\|_{L^2}^2)-
\int_{R^n} \int _0^{u_0} f(s)dsdx < d $ ($ d $ is the given constant). |
Keywords： |
Global solution, Blow up of the solution, Existence,
Nonexistence. |
Classification： |
35L05, 35L15, 35L70 |
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