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Ray solution of a backward–forward parabolic problem for data-handling systems

Published online by Cambridge University Press:  01 February 2000

CHARLES KNESSL
Affiliation:
Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 851 South Morgan Street, Chicago, IL 60607–7045, USA
JOSEPH B. KELLER
Affiliation:
Department of Mathematics and Mechanical Engineering, Stanford University, Stanford, CA 94305–2125, USA

Abstract

A problem for a backward–forward parabolic partial differential equation with a small diffusion coefficient ε is analyzed. The problem arises in describing the stochastic behaviour of a data-handling system with a large number of sources which turn on or off at random. We solve the problem asymptotically for ε small by using the ray method and the boundary layer method.

Type
Research Article
Copyright
2000 Cambridge University Press

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