Correction to: ``Weighted energy-dissipation approach to doubly nonlinear problems on the half line''
type: Item
instance of: scholarly article
title: Correction to: ``Weighted energy-dissipation approach to doubly nonlinear problems on the half line''
zbMATH Open document ID: 1480.58005
author: Goro Akagi
author: Stefano Melchionna
author: Ulisse Stefanelli
published in: Journal of Evolution Equations
publication date: 2022-01-06T00:00:00Z
review text: The authors consider the following Cauchy problem for the doubly nonlinear gradient flow posed on the dual space \(V^{*}\) of a uniformly convex Banach space \(V\) \[\xi(t)+\eta(t)=0,\ \xi(t)=d_{V}\psi(u'(t)),\ \eta(t)\in\partial\phi(u(t))\ \text{ in } V^{*} \text{ for } a.e.\ t>0, \leqno(1)\] \[u(0)=u_{0} \leqno(2)\] where \(d_{V}\psi:V\longrightarrow V^{*}\) (resp. \(\partial\phi:V\longrightarrow 2^{V^{*}}\)) denotes the G\(\hat{a}\)teaux derivative (resp. subdifferential) of a smooth (resp. lower semicontinuous) convex functional defined on \(V\). Under some suitable conditions, they prove that strong solutions of problem (1), (2) are recovered as a limit of minimizers of a WED functional. The obtained results generalize and correct earlier results published in 2018 in the same journal [\textit{G. Akagi} et al., J. Evol. Equ. 18, No. 1, 49--74 (2018; Zbl 1387.58021)].
reviewed by: Mohsen Timoumi
Mathematics Subject Classification ID: 58E30
Mathematics Subject Classification ID: 47J35
Mathematics Subject Classification ID: 35K92
Mathematics Subject Classification ID: 46B25
zbMATH DE Number: 7452701
zbMATH Keywords: doubly-nonlinear system
zbMATH Keywords: variational approach
zbMATH Keywords: WED functionals
zbMATH Keywords: causal limit
MaRDI profile type: Publication
full work available at URL: s00028-021-00698-y
OpenAlex ID: W3170393402
cites work: Weighted energy-dissipation functionals for doubly nonlinear evolution
cites work: Weighted energy-dissipation approach to doubly nonlinear problems on the half line
DOI: 10.1007/S00028-021-00698-Y
description: scientific article; zbMATH DE number 7452701