ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO DRIFT-DIFFUSION SYSTEM WITH GENERALIZED DISSIPATION

作者：Ogawa Takayoshi^*; Yamamoto Masakazu

来源：Mathematical Models and Methods in Applied Sciences, 2009, 19(6): 939-967.

DOI：10.1142/S021820250900367X

• Drift-diffusion system
• Keller-Segel equations
• large data global solutions
• decay of solution
• fractional order derivatives
• asymptotic profiles

We show the global existence and asymptotic behavior of solutions for the Cauchy problem of a nonlinear parabolic and elliptic system arising from semiconductor model. Our system has generalized dissipation given by a fractional order of the Laplacian. It is shown that the time global existence and decay of the solutions to the equation with large initial data. We also show the asymptotic expansion of the solution up to the second terms as t ->infinity.

• 出版日期2009-6