Premium
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.