The mixed initial-boundary value problem for diagonalizable quasilinear hyperbolic systems in the first quadrant |
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Authors: | Jianli Liu |
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Affiliation: | School of Mathematical Sciences, Fudan University, Shanghai 200433, China |
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Abstract: | In this paper, we investigate the mixed initial-boundary value problem for diagonalizable quasilinear hyperbolic systems with nonlinear boundary conditions on a half-unbounded domain . Under the assumptions that system is strictly hyperbolic and linearly degenerate, we obtain the global existence and uniqueness of C1 solutions with the bounded L1∩L∞ norm of the initial data as well as their derivatives and appropriate boundary condition. Based on the existence results of global classical solutions, we also prove that when t tends to infinity, the solutions approach a combination of C1 travelling wave solutions. Under the appropriate assumptions of initial and boundary data, the results can be applied to the equation of time-like extremal surface in Minkowski space R1+(1+n). |
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Keywords: | 35B40 35L50 35Q72 |
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