PreprintarXiv licencearXiv
A method of moving planes for a mixed local-nonlocal parabolic system with quenching
Abstract
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.
Related
- C1-estimates in nonlocal parabolic problems
- Harnack-type inequalities for nonlocal doubly nonlinear parabolic equations
- Interior regularity of mixed local-nonlocal parabolic semilinear equations
- Integral Harnack-type estimates and the rate of extinction for nonlocal doubly nonlinear parabolic equations
- Gradient self-improvement for mixed local and nonlocal parabolic equations
BibTeX
@misc{junquera2026method,
title = {{A method of moving planes for a mixed local-nonlocal parabolic system with quenching}},
author = {Sergio Junquera and Leandro M. Del Pezzo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08014},
eprint = {2610.08014},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08014},
}
RIS
TY - UNPB
TI - A method of moving planes for a mixed local-nonlocal parabolic system with quenching
AU - Sergio Junquera
AU - Leandro M. Del Pezzo
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.08014
UR - https://arxiv.org/abs/2610.08014
AB - 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 u_0, 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.
ER -