A pair of coupled nonlinear Volterra equations are examined for possible blow-up solutions. The system is motivated by certain models of explosion phenomena in a diffusive medium. Criteria for a blow-up to occur as well as bounds on the time of its occurrence are derived for a general class of nonlinearities. Specific results are obtained for two special cases involving power law and exponential nonlinearities. Also, the asymptotic growth rate near blow-up is determined for these two special cases when the kernel behaves like that of the one-dimension heat equation.
|Original language||English (US)|
|Number of pages||18|
|Journal||Journal of Integral Equations and Applications|
|State||Published - 1995|
ASJC Scopus subject areas
- Numerical Analysis
- Applied Mathematics