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Weakly coupled systems of parabolic Hamilton–Jacobi equations with Caputo time derivative

Abstract:

In this paper we prove existence and uniqueness of bounded viscosity solutions of weakly coupled systems of parabolic Hamilton–Jacobi equations with nonlocal ingredients, where the time evolution of each equation is driven by Caputo derivatives of different orders. As an application, we present steady-state large time behavior for the system in the case the stationary equation has uniqueness.