Growth rates for blow-up solutions of nonlinear Volterra equations-Reference-Cited by-同舟云学术

Growth rates for blow-up solutions of nonlinear Volterra equations

Published:1996 Issue:1 Volume:54 Page:153-159
ISSN:0033-569X
Container-title:Quarterly of Applied Mathematics
language:en
Short-container-title:Quart. Appl. Math.

Author:

Roberts Catherine A.,Olmstead W. E.

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics

Link

http://www.ams.org/qam/1996-54-01/S0033-569X-1996-1373844-5/S0033-569X-1996-1373844-5.pdf

Reference8 articles.

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3. D. Glenn Lasseigne and W. E. Olmstead, Ignition or nonignition of a combustible solid with marginal heating, Quart. Appl. Math. 43, 303–312 (1981)

4. 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)

5. 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)

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