Renormalized solutions for a non-local evolution equation with variable exponent

IF 2.5 2区数学 Q1 MATHEMATICS

Fractional Calculus and Applied Analysis Pub Date : 2025-05-22 DOI:10.1007/s13540-025-00425-1

Le Xuan Truong, Nguyen Thanh Long, Nguyen Ngoc Trong, Tan Duc Do

引用次数: 0

Abstract

We establish the existence and uniqueness of a renormalized solution to an evolution equation featuring the non-local fractional p(x, y)-Laplacian and nonnegative \(L^1\)-data. The definition of renormalized solutions is adapted to the non-local nature to bypass the use of chain rules which is unavailable. The fractional p(x, y)-Laplacian well encapsulates the fractional p-Laplacian with a constant exponent p. Hence our result extends [25] to the setting of variable exponents.

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一类变指数非局部演化方程的重整解

我们建立了具有非局部分数阶p(x, y)-拉普拉斯和非负\(L^1\) -数据的演化方程的重整解的存在唯一性。重整化解的定义适应了非局部性质，从而绕过了不可用的链式规则的使用。分数阶p(x, y)-拉普拉斯算子很好地封装了分数阶p-拉普拉斯算子的常数指数p。因此我们的结果将[25]扩展到可变指数的设置。

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

Fractional Calculus and Applied Analysis MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

4.70

自引率

16.70%

发文量

101

期刊介绍： Fractional Calculus and Applied Analysis (FCAA, abbreviated in the World databases as Fract. Calc. Appl. Anal. or FRACT CALC APPL ANAL) is a specialized international journal for theory and applications of an important branch of Mathematical Analysis (Calculus) where differentiations and integrations can be of arbitrary non-integer order. The high standards of its contents are guaranteed by the prominent members of Editorial Board and the expertise of invited external reviewers, and proven by the recently achieved high values of impact factor (JIF) and impact rang (SJR), launching the journal to top places of the ranking lists of Thomson Reuters and Scopus.