Monotone systems involving variable-order nonlocal operators
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 Perro...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2022 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:251833 |
| Acceso en línea: | https://ddd.uab.cat/record/251833 https://dx.doi.org/urn:doi:10.5565/PUBLMAT6612205 |
| Access Level: | acceso abierto |
| Palabra clave: | Viscosity solutions Hamilton-jacobi Variable-order nonlocal operators Comparison principles Large time behavior |
| Sumario: | 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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