Well-posedness of equations with fractional derivative
type: Item
instance of: scholarly article
title: Well-posedness of equations with fractional derivative
zbMATH Open document ID: 1213.47046
publication date: 2010-09-22T00:00:00Z
review text: The author studies the well-posedness for the equation \[ D^\alpha u(t)= Au(t)+ f(t),\quad 0\leq t\leq 2\pi, \] where \(A\) is a closed operator in a Banach space \(X\) and \(D^\alpha\), \(\alpha> 0\), is the fractional derivative in the sense of Weyl. Using known results on \(L^p\) multiplier theorems, the author gives necessary and/or sufficient conditions for the \(L^p\) well-posedness of the problem. The conditions involve the resolvent of \(A\) and the Rademacher boundedness. Corresponding results on the well-posedness of this problem are also obtained in periodic Besov spaces, periodic Triebel-Lizorkin spaces and periodic Hardy spaces.
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 46J15
Mathematics Subject Classification ID: 34K30
Mathematics Subject Classification ID: 42A45
Mathematics Subject Classification ID: 26A33
zbMATH DE Number: 5790096
zbMATH Keywords: well-posedness
zbMATH Keywords: fractional derivative
zbMATH Keywords: fractional Sobolev space
zbMATH Keywords: Fourier multipliers
zbMATH Keywords: Besov spaces
zbMATH Keywords: Triebel-Lizorkin spaces
author: Shangquan Bu
reviewed by: Dashan Fan
MaRDI profile type: Publication
full work available at URL: s10114-010-9231-z
OpenAlex ID: W2132536227
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DOI: 10.1007/S10114-010-9231-Z
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 5790096