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Local exact boundary controllability of entropy solutions to linearly degenerate quasilinear hyperbolic systems of conservation laws. (English) Zbl 1403.93042

Summary: In this paper, we study the local exact boundary controllability of entropy solutions to linearly degenerate quasilinear hyperbolic systems of conservation laws with characteristics of constant multiplicity. We prove the two-sided boundary controllability, the one-sided boundary controllability and the two-sided boundary controllability with fewer controls, by applying the strategy used in [T. Li and L. Yu, J. Math. Pures Appl. (9) 107, No. 1, 1–40 (2017; Zbl 1368.35180); L. Yu, Chin. Ann. Math., Ser. B 39, No. 6, 947–962 (2018; Zbl 1406.35191)]. Our constructive method is based on the well-posedness of semi-global solutions constructed by the limit of \(\varepsilon\)-approximate front tracking solutions to the mixed initial-boundary value problem with general nonlinear boundary conditions, and on some further properties of both \(\varepsilon\)-approximate front tracking solutions and limit solutions.

MSC:

93B05 Controllability
35L60 First-order nonlinear hyperbolic equations
93C05 Linear systems in control theory
93C20 Control/observation systems governed by partial differential equations
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