Author:
Ahmad Bashir,Alsaedi Ahmed,Berbiche Mohamed,Kirane Mokhtar
Abstract
We study the Cauchy problem for a system of semi-linear coupled fractional-diffusion equations with polynomial nonlinearities posed in \(\mathbb{R}_{+}\times \mathbb{R}^N\). Under appropriate conditions on the exponents and the orders of the fractional time derivatives, we present a critical value of the dimension N, for which global solutions with small data exist, otherwise solutions blow-up in finite time. Furthermore, the large time behavior of global solutions is discussed. For more information see https://ejde.math.txstate.edu/Volumes/2020/110/abstr.html
Reference42 articles.
1. C. Bandle, H. A. Levine, Q. S. Zhang; Critical exponents of Fujita type for inhomogeneous parabolic equations and systems, J. Math. Anal. Appl., 251 (2000), 624-648. https://doi.org/10.1006/jmaa.2000.7035
2. E. Bajlekova; Fractional Evolution Equations in Banach Spaces, PhD thesis, 2001, Technische Universiteit Eindhoven, DOI:10.6100/IR549476.
3. T. Cazenave, A. Haraux; An Introduction to Semilinear Evolution Equations, Oxford Lecture Series in Mathematics and its Applications, 1998.
4. K. Deng, H. A. Levine; The role of critical exponents in blow-up theorems, the sequel, J. Math. Anal. Appl., 243 (2000), 85-126. https://doi.org/10.1006/jmaa.1999.6663
5. J. I. Diaz, T. Pierantozzi, L. Vazquez; Finite time extinction for nonlinear fractional evolution equations and related properties, Electron. J. Differential Equations, Vol. 2016 (2016), No. 239, pp. 1-13.