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| LIFE-SPAN OF CLASSICAL SOLUTIONS TO QUASILINEAR HYPERBOLIC SYSTEMS WITH SLOWDECAY INITIAL DATA |
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Citation： |
KONG Dexing.LIFE-SPAN OF CLASSICAL SOLUTIONS TO QUASILINEAR HYPERBOLIC SYSTEMS WITH SLOWDECAY INITIAL DATA[J].Chinese Annals of Mathematics B,2000,21(4):413~440 |
| Page view： 1375
Net amount： 863 |
Authors： |
KONG Dexing; |
Foundation： |
Project supported by the National Natural Science Foundation of China. |
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| Abstract： |
The author considers the life-span of classical solutions to Cauchy problem for general first order quasilinear strictly hyperbolic systems in two independent variables with “slow” decay initial data. By constructing an example, first it is illustrated that the classical solution to this kind of Cauchy problem may blow up in a finite time, even if the system is weakly linearly degenerate. Then some lower bounds of the life-span of classical solutions are given in the case that the system is weakly linearly degenerate. These estimates imply that, when the system is weakly linearly degenerate, the classical solution exists almost globally in time. Finally, it is proved that Theorems 1.1-1.3 in [2] are still valid for this kind of initial data. |
Keywords： |
Quasilinear strictly hyperbolic system, Weak linear degeneracy, Cauchy problem, Classical solution, Life-span |
Classification： |
35L45, 35L67 |
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