A system of nonlinear volterra equations with blow-up solutions

C. M. Kirk; W. E. Olmstead; C. A. Roberts

doi:10.1216/JIE-2013-25-3-377

A system of nonlinear volterra equations with blow-up solutions

C. M. Kirk, W. E. Olmstead, C. A. Roberts

Engineering Sciences and Applied Mathematics

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

6 Scopus citations

Abstract

A pair of coupled nonlinear Volterra equations are examined for solutions that can have either global or blow-up behavior. The results represent an extension of the work in [8], where the analysis was restricted to cases in which the integral equations had identical kernels. Sufficient conditions are provided for global solutions as well as for blowup solutions. In the case of blow-up solutions, bounds on the blow-up time are derived. To demonstrate the applicability of the results, two examples are analyzed.

Original language	English (US)
Pages (from-to)	377-393
Number of pages	17
Journal	Journal of Integral Equations and Applications
Volume	25
Issue number	3
DOIs	https://doi.org/10.1216/JIE-2013-25-3-377
State	Published - Dec 1 2013

ASJC Scopus subject areas

Numerical Analysis
Applied Mathematics

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AB - A pair of coupled nonlinear Volterra equations are examined for solutions that can have either global or blow-up behavior. The results represent an extension of the work in [8], where the analysis was restricted to cases in which the integral equations had identical kernels. Sufficient conditions are provided for global solutions as well as for blowup solutions. In the case of blow-up solutions, bounds on the blow-up time are derived. To demonstrate the applicability of the results, two examples are analyzed.

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A system of nonlinear volterra equations with blow-up solutions

Abstract

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