Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • [1] N. Bleistein and R. A. Handelsman, Asymptotic Expansion of Integrals, Holt, Rinehardt, and Winston, New York, 1975
  • [2] D. Glenn Lasseigne and W. E. Olmstead, Ignition of a combustible solid by convection heating, J. Appl. Math. Phys. (ZAMP) 34, 886-898 (1983)
  • [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)
  • [6] W. E. Olmstead, S. Nemat-Nasser, and L. Ni, Shear bands as surfaces of discontinuity, J. Mech. Phys. Solids 42, 697-709 (1994)
  • [7] W. E. Olmstead, Ignition of a combustible half-space, SIAM J. Appl. Math. 43, 1-15 (1983)
  • [8] 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)

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 45D05

Retrieve articles in all journals with MSC: 45D05


Additional Information

DOI: https://doi.org/10.1090/qam/1373844
Article copyright: © Copyright 1996 American Mathematical Society


Brown University The Quarterly of Applied Mathematics
is distributed by the American Mathematical Society
for Brown University
Online ISSN 1552-4485; Print ISSN 0033-569X
© 2017 Brown University
Comments: qam-query@ams.org
AMS Website