Unique solvability of a Dirichlet problem for a fractional parabolic equation using energy-inequality method

IF 0.2 Q4 MATHEMATICS

Methods of Functional Analysis and Topology Pub Date : 2020-09-28 DOI:10.31392/mfat-npu26_3.2020.03

Benaoua Antara, Oussaeif Taki-Eddine, Rezzoug Imad

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引用次数: 5

Abstract

In this paper, we establish su cient conditions for the existence and uniqueness of the solution in fractional functional space for a class of initial boundaryvalue problems for a class of partial fractional parabolic di erential equations that include a fractional derivative of Caputo. The results are established by the application of the method based on a priori estimate "energy inequality" and the density of the range of the operator generated by the problem considered. áâ ®¢«¥÷ ¤®áâ â÷ ã¬®¢ ̈ ÷áã¢ ï â õ¤ ̈®áâ÷ à®§¢'ï§aã § ¤à®¡®¢®£® äãaæ÷® «ì®£® ̄à®áâ®àã ¤«ï ®¤®£® a« áã ̄®ç âa®¢®-aà ©®¢ ̈å § ¤ ç ¤«ï ¤¥ïa ̈å ¤à®¡®¢®̄ à ¡®«÷ç ̈å ¤ ̈ä¥à¥æ÷ «ì ̈å à÷¢ïì ÷§ ¤à®¡®¢®î ̄®å÷¤®î ̄ãâ®. ¥§ã«ìâ â ̈ ®âà ̈¬ ® è«ïå®¬ § áâ®áã¢ ï ¬¥â®¤ã ¥¥à£¥â ̈ç ̈å ¥à÷¢®áâ¥©. ®¢¥¤¥ é÷«ì÷áâì ®¡à §ã ® ̄¥à â®à , é® ¢÷¤ ̄®¢÷¤ õ § ¤ ç÷.

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用能量不等式方法求解分数阶抛物型方程Dirichlet问题的唯一可解性

本文建立了一类包含Caputo的分数阶导数的偏分数阶抛物型微分方程的一类初边值问题在分数函数空间中解的存在唯一性的充分条件。结果是通过应用基于先验估计“能量不等式”和所考虑问题产生的算子范围密度的方法建立的。¶®¶¶®啊！®¶776®áâà®⑪®什么®“®£® 项目®-是的。®£® tau®áâ®若昂®我不知道。®£® «áã»®帕森斯®“®-不©®¢§§§§776®什么®“®啊！®“776®什么®“®î®明天®î®. Í§“ìâ§776；®第776号® è“ïå®啊®对不起。®776®áâ©. ●®¶¶®¡§® •®à，é® ¶¶®我不知道。

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来源期刊

Methods of Functional Analysis and Topology MATHEMATICS-

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

25 weeks

期刊介绍： Methods of Functional Analysis and Topology (MFAT), founded in 1995, is a peer-reviewed arXiv overlay journal publishing original articles and surveys on general methods and techniques of functional analysis and topology with a special emphasis on applications to modern mathematical physics.