Correction to: ``Weighted energy-dissipation approach to doubly nonlinear problems on the half line''
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)].
scientific article; zbMATH DE number 7452701