Evolution equations and subdifferentials in Banach spaces
type: Item
instance of: scholarly article
title: Evolution equations and subdifferentials in Banach spaces
zbMATH Open document ID: 1058.35115
author: Goro Akagi
author: Mitsuharu Ôtani
published in: Discrete and Continuous Dynamical Systems
publication date: 2004-02-23T00:00:00Z
review text: The authors investigate the Cauchy problem \[ \frac{du}{dt}(t)+\partial \varphi^1(u(t))-\partial \varphi^2(u(t))\ni f(t),\quad 0<t<T\text{ in }V^*,\qquad u(0)=u_0,\tag{CP} \] where \(V^*\) is the dual space of a real reflexive Banach space \(V\). Under suitable assumptions on \(\varphi^1\) and \(\varphi^2\) it is proved the existence of the strong solutions of (CP). Applications to an initial-boundary value problem for the nonlinear heat equation are also presented.
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 47J35
Mathematics Subject Classification ID: 35D05
Mathematics Subject Classification ID: 35D10
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 47H04
zbMATH DE Number: 2046162
zbMATH Keywords: strong solution
zbMATH Keywords: local solution
zbMATH Keywords: global solution
zbMATH Keywords: \(p\)-Laplacian
zbMATH Keywords: Sobolev's critical exponent
reviewed by: Rodica Luca
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2046162