A mathematical problem from detonation theory
Author:
Wildon Fickett
Journal:
Quart. Appl. Math. 46 (1988), 459-471
MSC:
Primary 76L05; Secondary 73D05, 80A25
DOI:
https://doi.org/10.1090/qam/963582
MathSciNet review:
963582
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Abstract: A simplified abstraction of a partial-differential-equation problem which appears in the study of small perturbations on a detonation wave is studied. The interesting feature of this problem is that the function representing the unknown values of the dependent variable on one boundary appears as a source term in the partial differential equation. This unknown boundary function turns out to be the solution of an ordinary differential-difference equation. We study the properties of this differential-difference equation, and also present some representative solutions of the complete problem.
- Wildon Fickett, Approach to the steady solution for a plane Chapman-Jouguet detonation, Phys. Fluids A 1 (1989), no. 2, 371–379. MR 1021633, DOI https://doi.org/10.1063/1.857554
W. Fickett, Decay of small planar perturbations on a strong steady detonation: A simple differential-difference equation for the shock, Physics of Fluids 30, 1299–1309 (1987)
R. K. Brayton, Nonlinear oscillations in a distributed network, Quart. Appl. Math 24, 280–301 (1967)
- Kenneth L. Cooke and David W. Krumme, Differential-difference equations and nonlinear initial-boundary value problems for linear hyperbolic partial differential equations, J. Math. Anal. Appl. 24 (1968), 372–387. MR 232089, DOI https://doi.org/10.1016/0022-247X%2868%2990038-3
- Richard Bellman and Kenneth L. Cooke, Differential-difference equations, Academic Press, New York-London, 1963. MR 0147745
D. K. Frederick and A. B. Carlson, Linear systems in communication and control, Wiley, New York, 1971
W. Fickett and W. C. Davis, Detonation, Chapt. 2, University of California Press, Berkeley, 1979
W. Fickett, Decay of small planar perturbations on a strong steady detonation: A simple differential-difference equation for the shock, Physics of Fluids 30, 1299–1309 (1987)
R. K. Brayton, Nonlinear oscillations in a distributed network, Quart. Appl. Math 24, 280–301 (1967)
K. L. Cooke and D. Krumme, Differential-difference equations and nonlinear initial-boundary value problems for linear hyperbolic partial differential equations, J. Math. Anal. Appl. 24, 372–387 (1968)
R. Bellman and K. L. Cooke, Differential-difference equations, Academic Press, New York, 1963
D. K. Frederick and A. B. Carlson, Linear systems in communication and control, Wiley, New York, 1971
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Article copyright:
© Copyright 1988
American Mathematical Society
