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Boundary stabilization of quasilinear hyperbolic systems of balance laws: exponential decay for small source terms. (English) Zbl 1421.35213

The authors consider quasi-linear hyperbolic spatially 1D conservation laws with small source terms. There are two velocity-type variables on a segment. Boundary conditions are dynamical and describe tending of the boundary value to a fixed value. The authors prove that the solution tends to the steady solution provided that the source terms are sufficiently small and the initial distributions are close enough to that steady state.

MSC:

35L65 Hyperbolic conservation laws
35L50 Initial-boundary value problems for first-order hyperbolic systems
35L60 First-order nonlinear hyperbolic equations
76B75 Flow control and optimization for incompressible inviscid fluids
93D15 Stabilization of systems by feedback
35B40 Asymptotic behavior of solutions to PDEs
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References:

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