### 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 - 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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## Cite this

Suazo, E., Suslov, S., & Vega-Guzmán, J. M. (2011). The Riccati differential equation and a diffusion-type equation.

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