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Relaxation limit and global existence of smooth solutions of compressible Euler-Maxwell equations. (English) Zbl 1231.35039
Authors’ abstract: We consider smooth periodic solutions for the Euler-Maxwell equations, which are a symmetrizable hyperbolic system of balance laws. We proved that as the relaxation time tends to zero, the Euler-Maxwell system converges to the drift-diffusion equations at least locally in time. The global existence of smooth solutions is established near a constant state with an asymptotic stability property.

MSC:
35C20 Asymptotic expansions of solutions to PDEs
35B40 Asymptotic behavior of solutions to PDEs
35B10 Periodic solutions to PDEs
35B25 Singular perturbations in context of PDEs
35L60 First-order nonlinear hyperbolic equations
35Q35 PDEs in connection with fluid mechanics
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