Existence of global solutions and blow-up of solutions for coupled systems of fractional diffusion equations
Texas State University, Department of Mathematics
We study the Cauchy problem for a system of semi-linear coupled fractional-diffusion equations with polynomial nonlinearities posed in ℝ+ x ℝN. 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.
Coupled fractional-diffusion equations, Polynomial nonlinearities, Global solution, Blow-up
Ahmad, B., Alsaedi, A., Berbiche, M., & Kirane, M. (2020). Existence of global solutions and blow-up of solutions for coupled systems of fractional diffusion equations. <i>Electronic Journal of Differential Equations, 2020</i>(110), pp. 1-28.