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Compressible Euler-Maxwell equations. (English) Zbl 1019.82023
Summary: The Euler-Maxwell equations as a hydrodynamic model of charge transport of semiconductors in an electromagnetic field are studied. The global approximate solutions to initial-boundary value problem are constructed by the fractional Godunov scheme. The uniform bound and $$H^{-1}$$ compactness are proved. The approximate solutions are shown convergent by weak convergence methods. Then, with some new estimates due to the presence of electromagnetic fields, the existence of a global weak solution to the initial-boundary value problem is established for arbitrarily large initial data in $$L^\infty$$.

##### MSC:
 82D37 Statistical mechanical studies of semiconductors 35Q35 PDEs in connection with fluid mechanics 76X05 Ionized gas flow in electromagnetic fields; plasmic flow 78A35 Motion of charged particles 82C70 Transport processes in time-dependent statistical mechanics 82D10 Statistical mechanical studies of plasmas
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