The asymptotic behavior of globally smooth solutions of the multidimensional isentropic hydrodynamic model for semiconductors

Global Exponential Stability of Classical Solutions to the Hydrodynamic Model for Semiconductors

“…[1,7,8,9,10,14,18] and the references therein. For the evolutionary system (1.1)-(1.2), Luo, Natalini and Xin [14] first established the global exponential stability of small classical solutions to the Cauchy problem.…”

Asymptotic behaviour of global smooth solutionsto the multidimensional hydrodynamic model for semiconductors

“…In fact, the results of Section 2 and 3 hold also for the Cauchy problem. The remainder is to prove Proposition 1.1, which can be proved by modifying the proof of [10]. In particular, for the compact support initial data case, Proposition 1.1 can be proved by modifying proof of [22], where the local existence results for Cauchy problem of Euler-Poisson systems with compact support initial data were obtained.…”

“…Besides the local classical solutions obtained in Reference [16] and the steady-state solutions in the subsonic case studied in Reference [4], very few is known on the global solutions to the dynamic system (1). To provide some insights into the multidimensional evolutionary problem, the global existence and asymptotic behaviour of the spherically symmetrical solution of (1) were established in Reference [8] with = 1 and = {X ∈ R d : |0¡R 1 6|X |6R 2 ¡∞} and in Reference [9] with ¿1 and = {X ∈ R d : |X |¿R 1 ¿0}, respectively, where the pressure-density function p(n) is taken as p(n) = a 2 n ; n¿0; a = 0; ¿1 (2) Recently, the solution without any symmetry is studied in Reference [10] where the global existence and asymptotic behaviour of smooth solutions to the Cauchy problem of (1) are established under assumption (2) on p(n) and the assumption of b(X ) = constant.…”

Asymptotic stability of solutions to the nonisentropic hydrodynamic model for semiconductors

“…By applying the moment method and appropriate closure conditions, this system can be derived from the semiclassical Boltzmann equation coupled with the Poisson equation for the electric potential [13] . For the efforts put on the well-posedness of steady state solutions, global existence of classical or entropy weak solutions, zero relaxation limit problems and large time behavior of solutions for (1.1), we may refer to [1,2,5,[8][9][10][11] and their references therein. Physically, it is more important and more interesting to study (1.1) in the multidimensional case.…”