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Blow-up solutions to a system of nonlinear Volterra equations |
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| Authors: | W Mydlarczyk W Okrasiński CA Roberts |
| Institution: | a Institute of Mathematics, Technical University of Wroc?aw, 50-370 Wroc?aw, Wybrzeze Wyspiańskiego 27, Poland b Institute of Mathematics, University of Zielona Góra, 65-246 Zielona Góra, Podgórna 50, Poland c Department of Mathematics and Computer Science, College of the Holy Cross, Worcester, MA 01610, USA |
| Abstract: | A system of nonlinear Volterra integral equations with convolution kernels is considered. Estimates are given for the blow-up time when conditions are such that the solution is known to become unbounded in finite time. For two examples that arise in combustion problems, numerical estimates of blow-up time are presented. Additionally, the asymptotic behavior of the blow-up solution in the key limit is established for the power-law and exponential nonlinearity cases. |
| Keywords: | Volterra System of integral equations Explosion Blow-up time Asymptotic behavior |
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