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Erwin Suazo, Sergei K. Suslov, and José M. Vega-Guzmán
The Riccati differential equation and a diffusion-type equation view print
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| Published: |
January 30, 2011 |
| Keywords: |
The Cauchy initial value problem, heat kernel, fundamental solution, Riccati differential equation, diffusion-type equation |
| Subject: |
Primary 35C05, 35K15, 42A38. Secondary 35A08, 80A99 |
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Abstract
We 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.
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| 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 (DMS-0502349), the National Security Agency (DOD-H982300710096), the Sloan Foundation, and Arizona State University.
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| Author information
Erwin Suazo:
Department of Mathematical Sciences, University of Puerto Rico, Mayaguez, call box 9000, Puerto Rico 00681-9000.
erwin.suazo@upr.edu
Sergei K. Suslov:
School of Mathematical and Statistical Sciences, Mathematical, Computational and Modeling Sciences Center, Arizona State University, Tempe, AZ 85287-1804, U.S.A.
sks@asu.edu
José M. Vega-Guzmán:
Mathematical, Computational and Modeling Sciences Center, Arizona State University, Tempe, AZ 85287-1804, U.S.A.
jmvega@asu.edu
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