Asymptotic behavior of solutions to drift-diffusion system with generalized dissipation

Takayoshi Ogawa; Masakazu Yamamoto

doi:10.1142/S021820250900367X

Asymptotic behavior of solutions to drift-diffusion system with generalized dissipation

Takayoshi Ogawa, Masakazu Yamamoto

SCI - Mathematics

Research output: Contribution to journal › Article › peer-review

29 Citations (Scopus)

Abstract

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 → ∞.

Original language	English
Pages (from-to)	939-967
Number of pages	29
Journal	Mathematical Models and Methods in Applied Sciences
Volume	19
Issue number	6
DOIs	https://doi.org/10.1142/S021820250900367X
Publication status	Published - 2009 Jun

Keywords

Asymptotic profiles.
Decay of solution
Drift-diffusion system
Fractional order derivatives
Keller-Segel equations
Large data global solutions

ASJC Scopus subject areas

Modelling and Simulation
Applied Mathematics

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10.1142/S021820250900367X

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abstract = "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 → ∞.",

keywords = "Asymptotic profiles., Decay of solution, Drift-diffusion system, Fractional order derivatives, Keller-Segel equations, Large data global solutions",

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N2 - 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 → ∞.

AB - 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 → ∞.

KW - Asymptotic profiles.

KW - Decay of solution

KW - Drift-diffusion system

KW - Fractional order derivatives

KW - Keller-Segel equations

KW - Large data global solutions

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JO - Mathematical Models and Methods in Applied Sciences

JF - Mathematical Models and Methods in Applied Sciences

SN - 0218-2025

IS - 6

ER -

Asymptotic behavior of solutions to drift-diffusion system with generalized dissipation

Abstract

Keywords

ASJC Scopus subject areas

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