On initial value problem for elliptic equation on the plane under Caputo derivative

IF 2 3区数学 Q1 MATHEMATICS

Demonstratio Mathematica Pub Date : 2023-01-01 DOI:10.1515/dema-2022-0257

Tran Thanh Binh, Bui Dinh Thang, Nguyen Duc Phuong

引用次数: 0

Abstract

Abstract In this article, we are interested to study the elliptic equation under the Caputo derivative. We obtain several regularity results for the mild solution based on various assumptions of the input data. In addition, we derive the lower bound of the mild solution in the appropriate space. The main tool of the analysis estimation for the mild solution is based on the bound of the Mittag-Leffler functions, combined with analysis in Hilbert scales space. Moreover, we provide a regularized solution for our problem using the Fourier truncation method. We also obtain the error estimate between the regularized solution and the mild solution. Our current article seems to be the first study to deal with elliptic equations with Caputo derivatives on the unbounded domain.

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平面上Caputo导数下椭圆方程的初值问题

摘要本文主要研究Caputo导数下的椭圆型方程。基于输入数据的各种假设，我们得到了温和解的几个规律性结果。此外，我们还在适当的空间中导出了温和解的下界。温和解的分析估计的主要工具是基于Mittag-Leffler函数的界，结合Hilbert尺度空间的分析。此外，我们还利用傅里叶截断法给出了问题的正则化解。我们还得到了正则解与温和解之间的误差估计。我们目前的文章似乎是第一个研究无界区域上具有Caputo导数的椭圆方程。

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

Demonstratio Mathematica MATHEMATICS-

CiteScore

2.40

自引率

5.00%

发文量

审稿时长

35 weeks

期刊介绍： Demonstratio Mathematica publishes original and significant research on topics related to functional analysis and approximation theory. Please note that submissions related to other areas of mathematical research will no longer be accepted by the journal. The potential topics include (but are not limited to): -Approximation theory and iteration methods- Fixed point theory and methods of computing fixed points- Functional, ordinary and partial differential equations- Nonsmooth analysis, variational analysis and convex analysis- Optimization theory, variational inequalities and complementarity problems- For more detailed list of the potential topics please refer to Instruction for Authors. The journal considers submissions of different types of articles. "Research Articles" are focused on fundamental theoretical aspects, as well as on significant applications in science, engineering etc. “Rapid Communications” are intended to present information of exceptional novelty and exciting results of significant interest to the readers. “Review articles” and “Commentaries”, which present the existing literature on the specific topic from new perspectives, are welcome as well.