Volterra Equations Which Model Explosion in a Diffusive Medium
Document Type
Article
Publication Date
1993
DOI
10.1216/jiea/1181075776
Publication Title
Journal of Integral Equations and Applications
Volume
5
Issue
4
Pages
531-546
Abstract
An investigation is made of certain nonlinear Volterra integral equations which model explosive behavior in a diffusive medium. The basic results provide criteria involving the kernel and the nonlinearity for the solution to experience blow-up. Supporting examples from solid combustion and shear band formation are provided. Also, the connection is made with one-dimensional parabolic partial differential equations.
Rights
© 1993 Rocky Mountain Mathematics Consortium
"All articles published in JIEA become open access after five years from publication."
Original Publication Citation
Roberts, C. A., Lasseigne, D. G., & Olmstead, W. E. (1993). Volterra equations which model explosion in a diffusive medium. Journal of Integral Equations and Applications, 5(4), 531-546. https://doi.org/10.1216/jiea/1181075776
Repository Citation
Roberts, Catherine A.; Lasseigne, D. Glenn; and Olmstead, W. E., "Volterra Equations Which Model Explosion in a Diffusive Medium" (1993). Mathematics & Statistics Faculty Publications. 270.
https://digitalcommons.odu.edu/mathstat_fac_pubs/270