Global solutions for a nonlinear integral equation with a generalized heat kernel

Kazuhiro Ishige, Tatsuki Kawakami, Kanako Kobayashi

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

We study the existence and the large time behavior of global-intime solutions of a nonlinear integral equation with a generalized heat kernel u(x, t) = ∫RN G(x - y, t)φ(y)dy +∫t0 ZRN G(x - y, t - s)F(y, s, u(y, s), . . . ,δlu(y, s))dyds, where φ 2 ∈Wl,∞(RN) and l ∈ {0, 1, . . . }. The arguments of this paper are applicable to the Cauchy problem for various nonlinear parabolic equations such as fractional semilinear parabolic equations, higher order semilinear parabolic equations and viscous Hamilton-Jacobi equations.

Original languageEnglish
Pages (from-to)767-783
Number of pages17
JournalDiscrete and Continuous Dynamical Systems - Series S
Volume7
Issue number4
DOIs
Publication statusPublished - 2014 Aug 1

Keywords

  • Generalized heat kernel
  • Global solutions
  • Nonlinear integral equation
  • Semilinear parabolic equations
  • Weak Lr space

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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