与分数第一特征值相关的演化问题

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED Nonlinearity Pub Date : 2024-05-28 DOI:10.1088/1361-6544/ad4cd0

Begoña Barrios, Leandro Del Pezzo, Alexander Quaas and Julio D Rossi

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引用次数: 0

摘要

在本文中，我们研究了与第一个分数特征值相关的演化问题。我们证明，在粘性解的框架内，具有同质边界条件的迪里夏特问题对这个算子来说是很好解决的（问题具有解的存在性和唯一性，并且比较原理成立）。此外，我们还证明了解以指数级的速度衰减为零，其约束条件由我们同时研究的该问题的第一个特征值给出。

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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The evolution problem associated with the fractional first eigenvalue

In this paper we study the evolution problem associated with the first fractional eigenvalue. We prove that the Dirichlet problem with homogeneous boundary condition is well posed for this operator in the framework of viscosity solutions (the problem has existence and uniqueness of a solution and a comparison principle holds). In addition, we show that solutions decay to zero exponentially fast as with a bound that is given by the first eigenvalue for this problem that we also study.

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来源期刊

Nonlinearity 物理-物理：数学物理

CiteScore

3.00

自引率

5.90%

发文量

170

审稿时长

12 months

期刊介绍： Aimed primarily at mathematicians and physicists interested in research on nonlinear phenomena, the journal''s coverage ranges from proofs of important theorems to papers presenting ideas, conjectures and numerical or physical experiments of significant physical and mathematical interest. Subject coverage: The journal publishes papers on nonlinear mathematics, mathematical physics, experimental physics, theoretical physics and other areas in the sciences where nonlinear phenomena are of fundamental importance. A more detailed indication is given by the subject interests of the Editorial Board members, which are listed in every issue of the journal. Due to the broad scope of Nonlinearity, and in order to make all papers published in the journal accessible to its wide readership, authors are required to provide sufficient introductory material in their paper. This material should contain enough detail and background information to place their research into context and to make it understandable to scientists working on nonlinear phenomena. Nonlinearity is a journal of the Institute of Physics and the London Mathematical Society.

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