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| Asymptotic Stability of Equilibrium State to the Mixed Initial-Boundary Value Problem for Quasilinear Hyperbolic Systems |
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Citation： |
Yanzhao LI,Cunming LIU.Asymptotic Stability of Equilibrium State to the Mixed Initial-Boundary Value Problem for Quasilinear Hyperbolic Systems[J].Chinese Annals of Mathematics B,2015,36(3):323~344 |
| Page view： 1100
Net amount： 1155 |
Authors： |
Yanzhao LI; Cunming LIU; |
Foundation： |
supported by the National Natural Science Foundation of China(Nos.11326159,11401421);the China Postdoctoral Science Foundation(No.2014M560287);the Shanxi Scholarship Council of China(No.2013-045) |
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| Abstract： |
Under the internal dissipative condition, the Cauchy problem for inhomogeneous quasilinear hyperbolic systems with small initial data admits a unique global C1 solution, which exponentially decays to zero as t → +∞, while if the coefficient matrixΘ of boundary conditions satisfies the boundary dissipative condition, the mixed initialboundary value problem with small initial data for quasilinear hyperbolic systems with nonlinear terms of at least second order admits a unique global C1 solution, which also exponentially decays to zero as t → +∞. In this paper, under more general conditions, the authors investigate the combined effect of the internal dissipative condition and the boundary dissipative condition, and prove the global existence and exponential decay of the C1 solution to the mixed initial-boundary value problem for quasilinear hyperbolic systems with small initial data. This stability result is applied to a kind of models, and an example is given to show the possible exponential instability if the corresponding conditions are not satisfied. |
Keywords： |
Quasilinear hyperbolic system, Mixed initial-boundary value problem,Classical solution, Asymptotic stability |
Classification： |
35L40, 35L45 |
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