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The Cauchy–Neumann problem for a multi‐dimensional isentropic hydrodynamic model for semiconductors
Author(s) -
Li Yeping
Publication year - 2005
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.653
Subject(s) - mathematics , uniqueness , isentropic process , mathematical analysis , neumann boundary condition , cauchy problem , initial value problem , euler equations , boundary value problem , von neumann architecture , euler's formula , constant (computer programming) , pure mathematics , physics , thermodynamics , computer science , programming language
We investigate a multi‐dimensional isentropic hydrodynamic (Euler–Poisson) model for semiconductors, where the energy equation is replaced by the pressure–density relation p ( n ) . We establish the global existence of smooth solutions for the Cauchy–Neumann problem with small perturbed initial data and homogeneous Neumann boundary conditions. We show that, as t →+∞, the solutions converge to the non‐constant stationary solutions of the corresponding drift–diffusion equations. Moreover, we also investigate the existence and uniqueness of the stationary solutions for the corresponding drift–diffusion equations. Copyright © 2005 John Wiley & Sons, Ltd.