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2022 Monotone systems involving variable-order nonlocal operators
Miguel Yangari
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Publ. Mat. 66(1): 129-158 (2022). DOI: 10.5565/PUBLMAT6612205

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.

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Miguel Yangari. "Monotone systems involving variable-order nonlocal operators." Publ. Mat. 66 (1) 129 - 158, 2022. https://doi.org/10.5565/PUBLMAT6612205

Information

Received: 26 February 2020; Accepted: 3 December 2020; Published: 2022
First available in Project Euclid: 4 January 2022

Digital Object Identifier: 10.5565/PUBLMAT6612205

Subjects:
Primary: 35K41 , 47G20 , 49L25 , 60J75

Keywords: Comparison principles , Hamilton–Jacobi , Large time behavior , variable-order nonlocal operators , viscosity solutions

Rights: Copyright © 2022 Universitat Autònoma de Barcelona, Departament de Matemàtiques

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Vol.66 • No. 1 • 2022
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