MONOTONE SYSTEMS INVOLVING VARIABLE-ORDER NONLOCAL OPERATORS

Abstract:

In this paper, we study the existence and uniqueness of bounded viscosity solutions for parabolic Hamilton-Jacobi monotone systems in which the diffusion term is driven by variable-order nonlocal operators whose kernels depend on the space-time variable. We prove the existence of solutions via Perron's method, and considering Hamiltonians with linear and superlinear nonlinearities related to their gradient growth we state a comparison principle for bounded sub and supersolutions. Moreover, we present steady-state large time behavior with an exponential rate of convergence.

Año de publicación:

2022

Keywords:

• Large time behavior
• Viscosity solutions
• Hamilton-Jacobi
• Comparison principles
• Variable-order nonlocal operators

Fuente:

scopus