The Riccati differential equation and a diffusion-type equation

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

Research output: Contribution to journalArticle

12 Citations (Scopus)

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 - 2011

Fingerprint

Riccati Differential Equation
Elementary Functions
Heat Kernel
Characteristic Function
Explicit Solution
Variable Coefficients
Analytic Solution
Real Line
Initial Value Problem
Cauchy Problem
Limiting
Numerical Solution
Entire
Coefficient

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

The Riccati differential equation and a diffusion-type equation. / Suazo, Erwin; Suslov, Sergei; Vega-Guzmán, José M.

In: New York Journal of Mathematics, Vol. 17 A, 2011, p. 225-244.

Research output: Contribution to journalArticle

Suazo, Erwin ; Suslov, Sergei ; Vega-Guzmán, José M. / The Riccati differential equation and a diffusion-type equation. In: New York Journal of Mathematics. 2011 ; Vol. 17 A. pp. 225-244.
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