Antiperiodic problems for nonautonomous parabolic evolution equations
type: Item
instance of: scholarly article
title: Antiperiodic problems for nonautonomous parabolic evolution equations
zbMATH Open document ID: 1470.34160
DOI: 10.1155/2014/263690
author: Xianqiang Yang
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: This work focuses on the antiperiodic problem of nonautonomous semilinear parabolic evolution equation in the form \(u'(t) = A(t) u(t) + f(t, u(t))\), \(t \in \mathbb{R}\), \(u(t + T) = - u(t)\), \(t \in \mathbb{R}\), where \((A \left(t\right))_{t \in \mathbb{R}}\) (possibly unbounded), depending on time, is a family of closed and densely defined linear operators on a Banach space \(X\). Upon making some suitable assumptions such as the Acquistapace and Terreni conditions and exponential dichotomy on \((A \left(t\right))_{t \in \mathbb{R}}\), we obtain the existence results of antiperiodic mild solutions to such problem. The antiperiodic problem of nonautonomous semilinear parabolic evolution equation of neutral type is also considered. As sample of application, these results are applied to, at the end of the paper, an antiperiodic problem for partial differential equation, whose operators in the linear part generate an evolution family of exponential stability.
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 35B10
Mathematics Subject Classification ID: 35K20
Mathematics Subject Classification ID: 35K58
zbMATH DE Number: 7022042
Wikidata QID: Q59037283
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/263690
OpenAlex ID: W2000755160
cites work: Exact solution and interfacial tension of the six-vertex model with anti-periodic boundary conditions
cites work: The Onset and End of the Gunn Effect in Extrinsic Semiconductors
cites work: Fluctuation equations about classical field configurations and supersymmetric quantum mechanics
cites work: On the existence of periodic solutions to nonlinear abstract parabolic equations
cites work: On the existence of anti-periodic solutions to a nonlinear evolution equation associated with odd subdifferential operators
cites work: On the existence of anti-periodic solutions to nonlinear parabolic equations in noncylindrical domains
cites work: Anti-periodic solutions of some nonlinear evolution equations
cites work: Anti-periodic oscillations of some second-order differential equations and optimal control problems
cites work: Anti-periodic solutions to a class of nonlinear differential equations in Hilbert space
cites work: Anti-periodic solutions to nonlinear evolution equations
cites work: Anti-periodic solutions for evolution equations associated with maximal monotone mappings
cites work: Existence of anti-periodic mild solutions for semilinear evolution equations
cites work: Asymptotically periodic solutions to nonlocal Cauchy problems governed by compact evolution families
cites work: Antiperiodic solutions for dissipative evolution equations
cites work: Q5502497
cites work: Evolution operators and strong solutions of abstract linear parabolic equations
cites work: A unified approach to abstract linear nonautonomous parabolic equations
cites work: Q4327845
cites work: Semigroups of linear operators and applications to partial differential equations
cites work: Q4713492
cites work: Q3487858
cites work: One-Parameter Semigroups for Linear Evolution Equations
cites work: Geometric theory of semilinear parabolic equations
cites work: Q4453334
cites work: Anti-periodic solutions for semilinear evolution equations.
cites work: Q4063689
cites work: Q3847203
description: scientific article; zbMATH DE number 7022042