Global Existence and Asymptotic Limits of Weak Solutions of the Bipolar Hydrodynamic Model for Semiconductors

Abstract

For the case of the adiabatic exponents being larger than \(\), we establish the global existence of entropy weak solutions of the Cauchy problem to the bipolar hydrodynamic model for semiconductors. Using the theory of compensated compactness, we hence give finally a complete answer on the related existence problems with the “γ-law” pressure relation. A new kind of singular limit of the modified entropy weak solution is discussed. To some extent, the limit of this sort can provide some information about the uniform boundedness of the scaled solution sequences. The quasineutral-relaxation limit of the entropy weak solutions is also investigated.