 

Erwin Suazo, Sergei K. Suslov, and José M. VegaGuzmán
The Riccati differential equation and a diffusiontype equation view print


Published: 
January 30, 2011 
Keywords: 
The Cauchy initial value problem, heat kernel, fundamental solution, Riccati differential equation, diffusiontype equation 
Subject: 
Primary 35C05, 35K15, 42A38. Secondary 35A08, 80A99 


Abstract
We construct an explicit solution of the Cauchy initial value problem for
certain diffusiontype 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
timedependent coefficients. Some special and limiting cases are outlined.
Solution of the corresponding nonhomogeneous equation is also found.


Acknowledgements
This paper is written as a part of a summer program on analysis of the Mathematical and Theoretical Biology Institute (MTBI) at Arizona State University. The MTBI/SUMS Summer Undergraduate Research Program is supported by the National Science Foundation (DMS0502349), the National Security Agency (DODH982300710096), the Sloan Foundation, and Arizona State University.


Author information
Erwin Suazo:
Department of Mathematical Sciences, University of Puerto Rico, Mayaguez, call box 9000, Puerto Rico 006819000.
erwin.suazo@upr.edu
Sergei K. Suslov:
School of Mathematical and Statistical Sciences, Mathematical, Computational and Modeling Sciences Center, Arizona State University, Tempe, AZ 852871804, U.S.A.
sks@asu.edu
José M. VegaGuzmán:
Mathematical, Computational and Modeling Sciences Center, Arizona State University, Tempe, AZ 852871804, U.S.A.
jmvega@asu.edu

