Open Access
Translator Disclaimer
August 1999 Probabilistic methods for a linear reaction-hyperbolic system with constant coefficients
Elizabeth A. Brooks
Ann. Appl. Probab. 9(3): 719-731 (August 1999). DOI: 10.1214/aoap/1029962811


Linear reaction-hyperbolic systems of partial differential equations in one space dimension arise in the study of the physiological process by which materials are transported in nerve cell axons. Probabilistic methods are developed to derive a closed form approximate solution for an initial-boundary value problem of such a system. The approximate solution obtained is a translating solution of a heat equation. An estimate is proved giving the deviation of this approximate traveling wave solution from the exact solution.


Download Citation

Elizabeth A. Brooks. "Probabilistic methods for a linear reaction-hyperbolic system with constant coefficients." Ann. Appl. Probab. 9 (3) 719 - 731, August 1999.


Published: August 1999
First available in Project Euclid: 21 August 2002

zbMATH: 0959.60048
MathSciNet: MR1722280
Digital Object Identifier: 10.1214/aoap/1029962811

Primary: 0G99 , 35L45 , 35L50
Secondary: 92C20

Keywords: central limit theorem , Hyperbolic equations , renewal theory , Stochastic processes , Traveling waves

Rights: Copyright © 1999 Institute of Mathematical Statistics


Vol.9 • No. 3 • August 1999
Back to Top