## Journal of Integral Equations and Applications

- J. Integral Equations Applications
- Volume 25, Number 3 (2013), 377-393.

### A system of nonlinear Volterra equations with blow-up solutions

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

#### 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 [{\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.

#### Article information

**Source**

J. Integral Equations Applications, Volume 25, Number 3 (2013), 377-393.

**Dates**

First available in Project Euclid: 16 December 2013

**Permanent link to this document**

https://projecteuclid.org/euclid.jiea/1387207803

**Digital Object Identifier**

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

**Mathematical Reviews number (MathSciNet)**

MR3161618

**Zentralblatt MATH identifier**

1295.45005

#### Citation

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. https://projecteuclid.org/euclid.jiea/1387207803