The Riccati Differential Equation and a Diffusion-type Equation


We construct an explicit solution of the Cauchy initial value problem for certain diffusiontype equation with variable coefficients on the entire real line. The corresponding Green function (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 the second order linear differential equation with time-dependent coefficients. Some special and limiting cases are outlined. Solution of the corresponding nonhomogeneous equation is also found.

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@inproceedings{Suazo2008TheRD, title={The Riccati Differential Equation and a Diffusion-type Equation}, author={Erwin Suazo and JOS{\'E} M. VEGA-GUZM{\'A}N}, year={2008} }