One-sided exact boundary null controllability of entropy solutions to a class of hyperbolic systems of conservation laws |
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Authors: | Tatsien Li Lei Yu |
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Institution: | 1. School of Mathematical Sciences, Fudan University, Shanghai 200433, China;2. Shanghai Center for Mathematical Sciences, Fudan University, Shanghai 200433, China |
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Abstract: | In this paper, the one-sided exact boundary null controllability of entropy solutions is studied for a class of general strictly hyperbolic systems of conservation laws, whose negative (or positive) characteristic families are all linearly degenerate. The authors first prove the well-posedness of semi-global solutions constructed as the limit of ε-approximate front tracking solutions to the mixed initial-boundary value problem with general nonlinear boundary conditions and they establish various properties of both the ε-approximate front tracking solutions and such solutions. By means of essential modifications of the strategy suggested by the first author in 17] originally for the local exact boundary controllability in the framework of classical solutions, the one-sided local exact boundary null controllability of entropy solutions can then be realized via boundary controls acting on one side of the boundary, where the incoming characteristics are all linearly degenerate. |
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Keywords: | 35L60 35L65 35B37 Hyperbolic systems of conservation laws One-sided exact boundary controllability Semi-global entropy solution |
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