The Riccati differential equation and a diffusion-type equation

Erwin Suazo, Sergei Suslov, José M. Vega-Guzmán

Research output: Contribution to journalArticle

12 Scopus citations

Abstract

Construct an explicit solution of the Cauchy initial value problem for certain diffusion-type equations with variable coefficients on the entire real line. The heat kernel is given in terms of elementary functions and certain integrals involving a characteristic function, which should be found as an analytic or numerical solution of a Riccati differential equation with time-dependent coefficients. Some special and limiting cases are outlined. Solution of the corresponding nonhomogeneous equation is also found.

Original languageEnglish (US)
Pages (from-to)225-244
Number of pages20
JournalNew York Journal of Mathematics
Volume17 A
StatePublished - Sep 28 2011

Keywords

  • Diffusion-type equation
  • Fundamental solution
  • Heat kernel
  • Riccati differential equation
  • The cauchy initial value problem

ASJC Scopus subject areas

  • Mathematics(all)

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