Integrated semigroups and higher-order abstract equations
type: Item
instance of: scholarly article
title: Integrated semigroups and higher-order abstract equations
zbMATH Open document ID: 0915.34056
author: Liang Jin
author: Xiao Tijun
published in: Journal of Mathematical Analysis and Applications
publication date: 1999-07-12T00:00:00Z
review text: Let \(E\) be a Banach space and let \(B_0,B_1,\dots, B_{n-1}\) be closed linear operators on \(E\). Moreover, let \(f:[0,\infty)\to E\) be a given function. The authors study the wellposedness of the Cauchy problem for a higher-order abstract differential equation \[ u^{(n)}(t)+ \sum^{n- 1}_{i= 0} B_i u^{(i)}(t)= f(t)\quad (t\geq 0),\tag{1} \] \[ u^{(k)}(0)= u_k,\quad 0\leq k\leq n-1.\tag{2} \] The main tool used is the theory of \(r\)-times integrated semigroups. A few examples of applications to the theory of partial differential equations are presented.
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 47D03
Mathematics Subject Classification ID: 47E05
zbMATH DE Number: 1217003
zbMATH Keywords: linear operators
zbMATH Keywords: wellposedness
zbMATH Keywords: Cauchy problem
zbMATH Keywords: integrated semigroups
reviewed by: Józef Banaś
MaRDI profile type: Publication
full work available at URL: jmaa.1997.5909
OpenAlex ID: W2018602447
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DOI: 10.1006/JMAA.1997.5909
description: scientific article; zbMATH DE number 1217003