Global solutions for a strongly coupled fractional reaction-diffusion system in Marcinkiewicz spaces

Abstract

Abstract We prove the existence of solutions to the Cauchy problem for a strongly coupled semilinear reaction-diffusion system in Marcinkiewicz spaces L ( p 1 , ∞ ) × L ( p 2 , ∞ ) . The exponents p 1 , p 2 are chosen in a way that allows us to prove the existence of self-similar for this system. We present a fractional version of Yamazaki’s inequality, an essential tool that potentially applies to other fractional-in-time PDEs.