Journal of Integral Equations and Applications

A system of nonlinear Volterra equations with blow-up solutions

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

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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 [{\bf8}], 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 blow-up 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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J. Integral Equations Applications, Volume 25, Number 3 (2013), 377-393.

First available in Project Euclid: 16 December 2013

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Kirk, C.M.; Olmstead, W.E.; Roberts, C.A. A system of nonlinear Volterra equations with blow-up solutions. J. Integral Equations Applications 25 (2013), no. 3, 377--393. doi:10.1216/JIE-2013-25-3-377.

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