TOO MUCH REGULARITY MAY FORCE TOO MUCH UNIQUENESS

被引：124

作者：

Stynes, Martin ^{[1
]}

机构：

[1] Beijing Computat Sci Res Ctr, Appl & Computat Math Div, Beijing 100193, Peoples R China

来源：

FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2016年 / 19卷 / 06期

基金：

中国国家自然科学基金;

关键词：

fractional heat equation; fractional wave equation; regularity of solution; FRACTIONAL DIFFUSION EQUATION; WAVE EQUATIONS;

D O I：

10.1515/fca-2016-0080

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Time-dependent fractional-derivative problems Dt alpha u+Au= f are considered, where D-t(alpha) t is a Caputo fractional derivative of order a. (0, 1).(1, 2) and A is a classical elliptic operator, and appropriate boundary and initial conditions are applied. The regularity of solutions to this class of problems is discussed, and it is shown that assuming more regularity than is generally true-as many researchers do-places a surprisingly severe restriction on the problem.

引用

页码：1554 / 1562

页数：9

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