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

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  • Huang, Haochuan
  • Huang, Rui
  • Yin, Jingxue

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.

Suggested Citation

  • Huang, Haochuan & Huang, Rui & Yin, Jingxue, 2019. "The supplementation of the theory of periodic solutions for a class of nonlinear diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 753-766.
    • Handle: RePEc:eee:apmaco:v:346:y:2019:i:c:p:753-766
    DOI: 10.1016/j.amc.2018.10.070
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