The supplementation of the theory of periodic solutions for a class of nonlinear diffusion equations

Haochuan Huang, Rui Huang and Jingxue Yin

Applied Mathematics and Computation, 2019, vol. 346, issue C, 753-766

Abstract: In this paper, we provide supplementation of the theory of periodic solutions for a class of nonlinear diffusion equations ut−Δum=a(x,t)up with m > 0, p > 0. By using a new method to deal with the “blow up sequence”, we obtain the L∞ estimate with optimal exponent 11,pm≥1+2mN. In addition, we also give quite complete results about the existence of periodic solutions for the fast diffusion case 0 < m < 1. As far as we know, there are no results about the fast diffusion case before present work.

Keywords: Nonlinear diffusion equations; Periodic solutions; Existence (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:346:y:2019:i:c:p:753-766

DOI: 10.1016/j.amc.2018.10.070

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