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Large‐time behavior of solutions to the Rosenau equation with damped term
Author(s) -
Wang Yinxia,
Feng Gaihong
Publication year - 2017
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.4114
Subject(s) - mathematics , superposition principle , term (time) , initial value problem , mathematical analysis , nonlinear system , wave equation , diffusion equation , damped wave , diffusion , physics , economy , quantum mechanics , economics , service (business) , thermodynamics
In this paper, we consider the initial value problem for the Rosenau equation with damped term. The decay structure of the equation is of the regularity‐loss type, which causes the difficulty in high‐frequency region. Under small assumption on the initial value, we obtain the decay estimates of global solutions for n ≥1. The proof also shows that the global solutions may be approximated by the solutions to the corresponding linear problem for n ≥2. We prove that the global solutions may be approximated by the superposition of nonlinear diffusion wave for n = 1. Copyright © 2016 John Wiley & Sons, Ltd.