Growth rates for blow-up solutions of nonlinear Volterra equations
Authors:
Catherine A. Roberts and W. E. Olmstead
Journal:
Quart. Appl. Math. 54 (1996), 153-159
MSC:
Primary 45D05
DOI:
https://doi.org/10.1090/qam/1373844
MathSciNet review:
MR1373844
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Abstract: An investigation is made of the blow-up growth property of the solution to certain nonlinear Volterra integral equations which model explosive behavior in a diffusive medium. The basic results provide the asymptotic form of the blow-up solution for a large class of kernels as well as various nonlinearities based on examples from solid combustion and adiabatic shear band formation.
N. Bleistein and R. A. Handelsman, Asymptotic Expansion of Integrals, Holt, Rinehardt, and Winston, New York, 1975
D. Glenn Lasseigne and W. E. Olmstead, Ignition of a combustible solid by convection heating, J. Appl. Math. Phys. (ZAMP) 34, 886–898 (1983)
D. Glenn Lasseigne and W. E. Olmstead, Ignition or nonignition of a combustible solid with marginal heating, Quart. Appl. Math. 43, 303–312 (1981)
W. E. Olmstead and R. A. Handelsman, Asymptotic solution to a class of nonlinear Volterra integral equations, SIAM J. Appl. Math. 22, 373–384 (1972)
W. E. Olmstead and R. A. Handelsman, Asymptotic solution to a class of nonlinear Volterra integral equations. II, SIAM J. Appl. Math. 30, 180–189 (1976)
W. E. Olmstead, S. Nemat-Nasser, and L. Ni, Shear bands as surfaces of discontinuity, J. Mech. Phys. Solids 42, 697–709 (1994)
W. E. Olmstead, Ignition of a combustible half-space, SIAM J. Appl. Math. 43, 1–15 (1983)
Catherine A. Roberts, D. Glenn Lasseigne, and W. E. Olmstead, Volterra equations which model explosion in a diffusive medium, J. Integral Equations Appl. 5, 531–546 (1993)
N. Bleistein and R. A. Handelsman, Asymptotic Expansion of Integrals, Holt, Rinehardt, and Winston, New York, 1975
D. Glenn Lasseigne and W. E. Olmstead, Ignition of a combustible solid by convection heating, J. Appl. Math. Phys. (ZAMP) 34, 886–898 (1983)
D. Glenn Lasseigne and W. E. Olmstead, Ignition or nonignition of a combustible solid with marginal heating, Quart. Appl. Math. 43, 303–312 (1981)
W. E. Olmstead and R. A. Handelsman, Asymptotic solution to a class of nonlinear Volterra integral equations, SIAM J. Appl. Math. 22, 373–384 (1972)
W. E. Olmstead and R. A. Handelsman, Asymptotic solution to a class of nonlinear Volterra integral equations. II, SIAM J. Appl. Math. 30, 180–189 (1976)
W. E. Olmstead, S. Nemat-Nasser, and L. Ni, Shear bands as surfaces of discontinuity, J. Mech. Phys. Solids 42, 697–709 (1994)
W. E. Olmstead, Ignition of a combustible half-space, SIAM J. Appl. Math. 43, 1–15 (1983)
Catherine A. Roberts, D. Glenn Lasseigne, and W. E. Olmstead, Volterra equations which model explosion in a diffusive medium, J. Integral Equations Appl. 5, 531–546 (1993)
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Article copyright:
© Copyright 1996
American Mathematical Society
