Asymptotic expansions of solutions of fractional diffusion equations

Kazuhiro Ishige, Tatsuki Kawakami, Hironori Michihisa

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

Abstract

In this paper we obtain the precise description of the asymptotic behavior of the solution u of the fractional diffusion equation ∂tu + (-Δ)θ/2 u = 0 in RN × (0,∞) with the initial data φ ∈ LK := L1(RN, (1 + |x|)K dx), where 0 < θ < 2 and K ≥ 0. This enables us to obtain the asymptotic behavior of the hot spots of the solution u. Furthermore, we develop the arguments in [K. Ishige and T. Kawakami, Math. Ann., 353 (2012), pp. 161-192] and [K. Ishige, T. Kawakami, and K. Kobayashi, J. Evol. Equ., 14 (2014), pp. 749-777] and establish a method to obtain the asymptotic expansions of the solutions to inhomogeneous fractional diffusion equations and nonlinear fractional diffusion equations.

Original languageEnglish
Pages (from-to)2167-2190
Number of pages24
JournalSIAM Journal on Mathematical Analysis
Volume49
Issue number3
DOIs
Publication statusPublished - 2017 Jan 1

Keywords

  • Anomalous diffusion
  • Asymptotic expansion
  • Fractional diffusion equation
  • Hot spot
  • Semilinear parabolic equation

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

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