We discuss the stability of the steady state solutions for an isentropic hydrodynamic model of semiconductors of two species. We consider not only the mass and momentum equations for electrons, but also those two equations for holes. The recombination effects between electrons and holes are taken into consideration as well. We study the case where the doping profile is close to zero and depends on the spacial variable x. We shall show that steady state solutions are asymptotically stable.
Academic Press
We consider the Riemann problem for a system of conservation laws related to a phase transition problem. The system is nonisentropic and we treat the case where the latent heat is not zero. We study the cases where the initial data are given in the same phase and in the different phases. The role of the entropy condition is studied as well as the kinetic relation and the entropy rate admissibility criterion. We confine our attention to the case where the speeds of phase boundaries are close to zero. This is one interesting case in physics. We discuss the number of phase boundaries consistent with the above criteria and the uniqueness and nonuniqueness issue of the solution to the Riemann problem. r 2004 Elsevier Inc. All rights reserved.
We study the asymptotic behavior of the solution for a hydrodynamic model of semiconductors where the energy equation is included. We study the case where the flow is subsonic and the doping profile is close to a negative constant, depending on the spacial variable x. We shall show that a given steady state solution is asymptotically stable or unstable depending on whether or not the density of the initial data satisfies P =0, where P is defined in (3.5).
0. Introduction. In this paper we study the nonexistence of global smooth solutions of one-dimensional motions for nonlinear viscoelastic fluids and solids by the method of Rozhdestvenskii [1], This method has been applied to prove the nonexistence of global smooth solutions for the shearing motions in an elastic circular tube in [2].It is well known that the quasilinear hyperbolic equation showed the existence of a global smooth solution for small initial data, and conjectured the breakdown of smooth solutions for large initial data. The effect of fading memory for elastic materials causing a dissipative mechanism is included in this model as the stress functional in the stress-strain relation. I shall show the breakdown of smooth solutions in this problem in Sec. 2.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.