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LARGE-TIME BEHAVIOUR OF THE SOLUTIONS FOR A MULTIDIMENSIONAL NON-ISENTROPIC HYDRODYNAMIC MODEL FOR SEMICONDUCTORS

Published online by Cambridge University Press:  02 February 2006

Yeping Li
Yeping Li
Affiliation:
Department of Mathematics, Xianning College, Xianning, China ([email protected])
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Abstract

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We investigate the multidimensional non-isentropic Euler–Poisson (or full hydrodynamic) model for semiconductors, which contain an energy-conserved equation with non-zero thermal conductivity coefficient. We first discuss existence and uniqueness of the non-constant stationary solutions to the corresponding drift–diffusion equations. Then we establish the global existence of smooth solutions to the Cauchy problem with initial data, which are close to the stationary solutions. We find that these smooth solutions tend to the stationary solutions exponentially fast as $t\rightarrow+\infty$.

Keywords

Primary 35L6576X0535M1035L7035Q72large-time behavioursmooth solutionsmultidimensionalnon-isentropic hydrodynamic modelsemiconductors
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 49 , Issue 1 , February 2006 , pp. 145 - 172
Copyright
Copyright © Edinburgh Mathematical Society 2006