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Construction of boundary conditions for hyperbolic relaxation approximations. I: The linearized Suliciu model. (English) Zbl 1450.35166

Summary: Starting with this paper, we intend to develop a program aiming at construction of boundary conditions (BCs) for hyperbolic relaxation systems. Physically, such BCs are not always available. The construction is based on the assumption that the relaxation systems and well-posed BCs for the corresponding equilibrium systems are given. This paper focuses on the linearized Suliciu model. We obtain strictly dissipative and compatible BCs for the linearized model with different non-characteristic boundaries. Moreover, the effectiveness of the constructed BCs is shown by resorting to formal asymptotic solutions and energy estimates.

MSC:

35L50 Initial-boundary value problems for first-order hyperbolic systems
35L60 First-order nonlinear hyperbolic equations
35Q35 PDEs in connection with fluid mechanics
76N20 Boundary-layer theory for compressible fluids and gas dynamics
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