Global weakly discontinuous solutions to quasilinear hyperbolic systems of conservation laws with damping with a kind of non-smooth initial data |
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Authors: | Zhi-Qiang Shao Ya-Chun Li De-Xing Kong |
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Institution: | (1) Department of Mathematics, Fuzhou University, Fuzhou, 350002, China;(2) Department of Mathematics, Shanghai Jiao Tong University, Shanghai, 200030, China |
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Abstract: | For the Cauchy problem with a kind of non-smooth initial data for weakly linearly degenerate hyperbolic systems of conservation
laws with the linear damping term, we prove the existence and uniqueness of global weakly discontinuous solution u = u(t, x) containing only n weak discontinuities with small amplitude on t ≥ 0, and this solution possesses a global structure similar to that of the similarity solution of the corresponding homogeneous Riemann problem. As an application of our result, we obtain the existence and uniqueness
of global weakly discontinuous solution, continuous and piecewise C
1 solution with discontinuous first order derivatives, of the flow equations of a model class of fluids with viscosity induced
by fading memory.
De-Xing Kong: Supported by the National Science Foundation of China(Grant 10371073), the Special Funds for Major State Basic
Research Projects of China (Grant 2000077306), the Qi Ming Xing programme of Shanghai Government, and the Project sponsored
by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, the Ministry of Education of China. |
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Keywords: | " target="_blank"> Cauchy problem hyperbolic system of conservation laws with damping global weakly discontinuous solution weakly linear degeneracy |
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