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Smooth Solution and Its Large Time Behavior to Multi-Dimensional Lyumkis Energy Transport Model in Semiconductor Science

by Chen, L., Hsiao, L., Warnecke, G..

Series: 2002-36, Preprints

35M10 Equations of mixed type
35K55 Nonlinear parabolic equations
35K65 Degenerate parabolic equations
78A35 Motion of charged particles

The global existence and large time behavior of smooth solution to the initial boundary
value problem for the multi -dimensional Lyumkis energy transport model in semiconductor
science are discussed in this paper. Under the insulating boundary condition, when the initial
data are a small pertubation of an isothermal stationary solution, the smooth solution of
the problem converges to that stationary solution exponentially fast as time goes to infinity.

Lyumkis energy transport model, globel existence, asymptotic behavior, strong