On a nonlinear equation with fractional derivative

E. I. Kaikina, P. I. Naumkin, N. Hayashi

Research output: Contribution to journalArticlepeer-review

Abstract

We consider a nonlinear equation with fractional derivative in which the nonlinearity has the form of a linear combination of convective and nonconvective types. We prove the time-global existence of solutions of the Cauchy problem and find their asymptotics at large times uniformly with respect to the space variable. The proof method is based on a detailed investigation of the behavior of the Green function, which permits one to drop the restriction of smallness of the initial data in the case of a nonlinearity of special form.

Original languageEnglish
Pages (from-to)83-100
Number of pages18
JournalDifferential Equations
Volume46
Issue number1
DOIs
Publication statusPublished - 2010 Mar
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Mathematics(all)

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