Large‐time behavior of solutions to the Rosenau equation with damped term |
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Authors: | Yinxia Wang Gaihong Feng |
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Institution: | 1. School of Mathematics Information Sciences, North China University of Water Resources and Electric Power, Zhengzhou, China;2. Shengda Economics and Management College of Zhengzhou, Zhengzhou, China |
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Abstract: | 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. |
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Keywords: | Rosenau equation with hydrodynamical damped term initial value problem decay estimate large‐time behavior |
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