Monotone systems involving variable-order nonlocal operators

IF 0.8 3区数学 Q2 MATHEMATICS

Publicacions Matematiques Pub Date : 2022-01-01 DOI:10.5565/publmat6612205

Miguel Yangari

引用次数: 0

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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变阶非局部算子的单调系统

本文研究了扩散项由核依赖于时空变量的变阶非局部算子驱动的抛物型Hamilton-Jacobi单调系统有界黏性解的存在唯一性。利用Perron方法证明了解的存在性，并在考虑线性和超线性非线性与梯度增长有关的情况下，给出了有界下解和超解的比较原理。此外，我们还给出了具有指数收敛速率的稳态大时间行为。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Publicacions Matematiques 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publicacions Matemàtiques is a research mathematical journal published by the Department of Mathematics of the Universitat Autònoma de Barcelona since 1976 (before 1988 named Publicacions de la Secció de Matemàtiques, ISSN: 0210-2978 print, 2014-4369 online). Two issues, constituting a single volume, are published each year. The journal has a large circulation being received by more than two hundred libraries all over the world. It is indexed by Mathematical Reviews, Zentralblatt Math., Science Citation Index, SciSearch®, ISI Alerting Services, COMPUMATH Citation Index®, and it participates in the Euclid Project and JSTOR. Free access is provided to all published papers through the web page. Publicacions Matemàtiques is a non-profit university journal which gives special attention to the authors during the whole editorial process. In 2019, the average time between the reception of a paper and its publication was twenty-two months, and the average time between the acceptance of a paper and its publication was fifteen months. The journal keeps on receiving a large number of submissions, so the authors should be warned that currently only articles with excellent reports can be accepted.