Optimal convergence rates to nonlinear diffusion waves for the compressible Euler-Poisson system with damping

Hongfang Ma

doi:10.1016/j.jmaa.2010.04.047

Optimal convergence rates to nonlinear diffusion waves for the compressible Euler-Poisson system with damping

Hongfang Ma

Department of Mathematics

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

Abstract

In this work, we study the 1-D isentropic bipolar hydrodynamic model. This model takes the form of compressible Euler-Poisson system with nonlinear damping added to the momentum equations. Under some smallness conditions, the solutions to the Cauchy problem of the system globally exist and convergence to the nonlinear diffusion waves, which are the corresponding solutions of nonlinear parabolic equations given by the Darcy's law with a specified initial data. The optimal convergence rates are obtained by Green function method when the initial perturbation is in L¹-space. © 2010 Elsevier Inc.

Original language	English
Pages (from-to)	511-529
Journal	Journal of Mathematical Analysis and Applications
Volume	370
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2010.04.047
Publication status	Published - Oct 2010

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Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

Research Keywords

Euler-Poisson system
Green function method
Nonlinear damping
Optimal convergence rates

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title = "Optimal convergence rates to nonlinear diffusion waves for the compressible Euler-Poisson system with damping",

abstract = "In this work, we study the 1-D isentropic bipolar hydrodynamic model. This model takes the form of compressible Euler-Poisson system with nonlinear damping added to the momentum equations. Under some smallness conditions, the solutions to the Cauchy problem of the system globally exist and convergence to the nonlinear diffusion waves, which are the corresponding solutions of nonlinear parabolic equations given by the Darcy's law with a specified initial data. The optimal convergence rates are obtained by Green function method when the initial perturbation is in L1-space. {\textcopyright} 2010 Elsevier Inc.",

keywords = "Euler-Poisson system, Green function method, Nonlinear damping, Optimal convergence rates",

author = "Hongfang Ma",

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N2 - In this work, we study the 1-D isentropic bipolar hydrodynamic model. This model takes the form of compressible Euler-Poisson system with nonlinear damping added to the momentum equations. Under some smallness conditions, the solutions to the Cauchy problem of the system globally exist and convergence to the nonlinear diffusion waves, which are the corresponding solutions of nonlinear parabolic equations given by the Darcy's law with a specified initial data. The optimal convergence rates are obtained by Green function method when the initial perturbation is in L1-space. © 2010 Elsevier Inc.

AB - In this work, we study the 1-D isentropic bipolar hydrodynamic model. This model takes the form of compressible Euler-Poisson system with nonlinear damping added to the momentum equations. Under some smallness conditions, the solutions to the Cauchy problem of the system globally exist and convergence to the nonlinear diffusion waves, which are the corresponding solutions of nonlinear parabolic equations given by the Darcy's law with a specified initial data. The optimal convergence rates are obtained by Green function method when the initial perturbation is in L1-space. © 2010 Elsevier Inc.

KW - Euler-Poisson system

KW - Green function method

KW - Nonlinear damping

KW - Optimal convergence rates

UR - https://www.scopus.com/pages/publications/77953574640

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-77953574640&origin=recordpage

U2 - 10.1016/j.jmaa.2010.04.047

DO - 10.1016/j.jmaa.2010.04.047

M3 - RGC 21 - Publication in refereed journal

SN - 0022-247X

VL - 370

SP - 511

EP - 529

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Optimal convergence rates to nonlinear diffusion waves for the compressible Euler-Poisson system with damping

Abstract

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Research Keywords

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