### 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 language | English (US) |
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Pages (from-to) | 225-244 |

Number of pages | 20 |

Journal | New York Journal of Mathematics |

Volume | 17 A |

State | Published - 2011 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*New York Journal of Mathematics*,

*17 A*, 225-244.

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

Research output: Contribution to journal › Article

*New York Journal of Mathematics*, vol. 17 A, pp. 225-244.

}

TY - JOUR

T1 - The Riccati differential equation and a diffusion-type equation

AU - Suazo, Erwin

AU - Suslov, Sergei

AU - Vega-Guzmán, José M.

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

KW - Diffusion-type equation

KW - Fundamental solution

KW - Heat kernel

KW - Riccati differential equation

KW - The cauchy initial value problem

UR - http://www.scopus.com/inward/record.url?scp=80053113773&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80053113773&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:80053113773

VL - 17 A

SP - 225

EP - 244

JO - New York Journal of Mathematics

JF - New York Journal of Mathematics

SN - 1076-9803

ER -