MR2493875
Ryo KOBAYASHI and Shuichi KAWASHIMA
Ryo KOBAYASHI and Shuichi KAWASHIMA
Decay Estimates and Large Time Behavior of Solutions to the Drift-Diffusion System
Funkcialaj Ekvacioj. Serio Internacia
51
2008
371--394
http://fe.math.kobe-u.ac.jp/FE/FullPapers/51-3/51_371.pdf
http://www.ams.org/mathscinet-getitem?mr=MR2493875
We study the drift-diffusion system arising in the semiconductor device simulation and the plasma physics. We consider the initial value problem for this system and derive the optimal $L^p$ decay estimate of solutions by applying the time weighted $L^p$ energy method. Furthermore, we show that the solutions approach the corresponding heat kernels as time tends to infinity. This asymptotic result is based on the optimal $L^p-L^q$ decay estimate for the linearized problem.
Drift-diffusion system, Decay estimate, Large time behavior, Time weighted energy method, $L^p-L^q$ estimate.
35B40, 35M20, 82D37.
51-371
2008
Decay Estimates and Large Time Behavior of Solutions to the Drift-Diffusion System
Ryo KOBAYASHI and Shuichi KAWASHIMA
Ryo KOBAYASHI and Shuichi KAWASHIMA
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