Existence of stationary solutions for some systems of integro-differential equations with superdiffusion

Vitali Vougalter (1) , Vitaly Volpert (2, 3)

1 Department of Mathematics [University of Toronto]
2 DRACULA - Multi-scale modelling of cell dynamics : application to hematopoiesis
3 MMCS - Modélisation mathématique, calcul scientifique

In this article, we establish the existence of solutions of a system of integro-differential equations arising in population dynamics in the case of anomalous diffusion. The proof of the existence of solutions is based on a fixed point technique. Solvability conditions for elliptic operators without the Fredholm property in unbounded domains are used.

Domaines: Equations aux dérivées partielles [math.AP]

Vitali Vougalter, Vitaly Volpert. Existence of stationary solutions for some systems of integro-differential equations with superdiffusion. Rocky Mountain Journal of Mathematics, 2017, 47 (3), pp.955-970. ⟨10.1216/RMJ-2017-47-3-955⟩. ⟨hal-01564763⟩