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.


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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