Diffusive Relaxation Limits Of Compressible Euler-Maxwell Equations

This thesis is concerned with the diffusive relaxation limits of compressible Euler-Maxwellequations, which take the form of non-isentropic Euler equations for the conservation laws of massdensity, current density and energy density for electrons, coupled to Maxwell’s equations forself-consistent electromagnetic field. The thesis is divided into five chapters.In the first chapter, we first introduce the Euler-Maxwell equations and give the recentdevelopment for this model. Inspired by the Maxwell’s iteration idea, we present the convergencefrom the Euler-Maxwell equations to the drift-diffusion equations in a formal level. To justify theasymptotic process rigorously, there are some technical difficulties which need to be overcome.Finally, the main results are given.In the second chapter, we first rewrite Euler–Maxwell equations as a symmetrizable hyperbolicsystem. Then we review some useful conclusions and a continuous principle for singular limitproblems of quasi-linear symmetrizable hyperbolic systems.In the third chapter, we construct new approximations inspired by Maxwell-type iteration andpresent the quantity estimates of error by a lemma, which is used to prove the main results.In the fourth chapter, from the error equations, we give the rigorous proof of main results by usingthe error energy methods.In the fifth chapter, we present the further prospect on the problem.