Growth rates for blow-up solutions of nonlinear Volterra equations

Catherine A. Roberts; W. E. Olmstead

doi:10.1090/qam/1373844

Growth rates for blow-up solutions of nonlinear Volterra equations

Catherine A. Roberts^*, W. E. Olmstead

^*Corresponding author for this work

Engineering Sciences and Applied Mathematics

Research output: Contribution to journal › Article › peer-review

31 Scopus citations

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.

Original language	English (US)
Pages (from-to)	153-159
Number of pages	7
Journal	Quarterly of Applied Mathematics
Volume	54
Issue number	1
DOIs	https://doi.org/10.1090/qam/1373844
State	Published - Mar 1996

ASJC Scopus subject areas

Applied Mathematics

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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.",

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