Existence and asymptotic behavior of global smooth solution for  p ‐system with nonlinear damping and fixed boundary effect | Zendy

Jiang Mina | Zendy; Zhang Yinghui | Zendy

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Existence and asymptotic behavior of global smooth solution for p ‐system with nonlinear damping and fixed boundary effect

Author(s) -

Jiang Mina,

Zhang Yinghui

Publication year - 2013

Publication title -

mathematical methods in the applied sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.719

H-Index - 65

eISSN - 1099-1476

pISSN - 0170-4214

DOI - 10.1002/mma.2998

Subject(s) - mathematics , nonlinear system , boundary value problem , mathematical analysis , function (biology) , boundary (topology) , initial value problem , physics , quantum mechanics , evolutionary biology , biology

This paper is concerned with the initial boundary value problem for the p ‐system with nonlinear damping and fixed boundary condition. We show that the corresponding problem admits a unique global solution, and such a solution tends time asymptotically to the corresponding nonlinear diffusion wave governed by the classical Darcy's law provided that the corresponding prescribed initial error function is sufficiently small. Copyright © 2013 John Wiley & Sons, Ltd.

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