A method of moving planes for a mixed local-nonlocal parabolic system with quenching
Resumen:
In this paper we develop a parabolic version of the method of moving planes on systems with a mixed local and nonlocal diffusion operator, that being L=−(−Δ)s+Δ, where (−Δ)s is the integral fractional laplacian. We then use this result to study the quenching phenomena occurring in said systems with a singular absorption term of the type (1−u)−p. We prove that there exists a range of multiplicative parameters for which every solution presents quenching, and that for any initial datum u0, there exists a small enough multiplicative parameter such as the solution is globally defined. We also prove that the quenching phenomena cannot happen arbitrarily close to the boundary, but they are contained in a compact subset of the domain.
| 2026 | |
| Agencia Nacional de Investigación e Innovación | |
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Quenching Moving planes Mixed operator Nonlocal diffusion Fractional laplacian Ciencias Naturales y Exactas Matemáticas |
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| Inglés | |
| Agencia Nacional de Investigación e Innovación | |
| REDI | |
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https://hdl.handle.net/20.500.12381/5716
https://doi.org/10.48550/arXiv.2610.08014 |
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| Acceso abierto | |
| Reconocimiento 4.0 Internacional. (CC BY) |
