Abstract
Abstract
In this paper, we study a coupled systems of parabolic equations subject to large initial data. By using comparison principle and Kaplan’s method, we get the upper and lower bound for the life span of the solutions.
Funder
College of Science, China Pharmaceutical University
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory,Analysis
Reference20 articles.
1. Friedman, A., Giga, Y.: A single point blow-up for solutions of semilinear parabolic systems. J. Fac. Sci., Univ. Tokyo, Sect. 1A, Math. 34, 65–79 (1987)
2. Fujita, H.: On the blowing up of solutions of the Cauchy problem for $u_{t}=\Delta u+u^{1+\alpha }$. J. Fac. Sci., Univ. Tokyo, Sect. 1A, Math. 16, 105–113 (1966)
3. Friedman, A., Lacey, A.: The blow-up time of solutions of nonlinear heat equation with small diffusion. SIAM J. Math. Anal. 18, 711–721 (1987)
4. Gui, C.F., Wang, X.F.: Life span of solutions of the Cauchy problem for a semilinear heat equation. J. Differ. Equ. 115, 166–172 (1995)
5. Lee, T.Y., Ni, W.: Global existence, large time behavior and life span of solutions of a semilinear parabolic Cauchy problem. Trans. Am. Math. Soc. 333, 1434–1446 (1992)