Global existence for vector valued fractional reaction-diffusion equations
Provides theoretical guarantees for global solutions in fractional reaction-diffusion systems, relevant for mathematical biology and pattern formation.
The paper proves global existence of solutions for infinite dimensional fractional reaction-diffusion equations using time-splitting methods and convex invariant regions, with applications to biological and pattern formation systems.
In this paper, we study the initial value problem for infinite dimensional fractional non-autonomous reaction-diffusion equations. Applying general time-splitting methods, we prove the existence of solutions globally defined in time using convex sets as invariant regions. We expose examples, where biological and pattern formation systems, under suitable assumptions, achieve global existence. We also analyze the asymptotic behavior of solutions.