Monotone systems involving variable-order nonlocal operators

• Autores: Miguel Yangari
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 66, Nº 1, 2022, págs. 129-158
• Idioma: inglés
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• Resumen

  • 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.