Global existence and maximal regularity of solutions of gradient systems
type: Item
instance of: scholarly article
title: Global existence and maximal regularity of solutions of gradient systems
zbMATH Open document ID: 1209.47020
author: Sahbi Boussandel
published in: Journal of Differential Equations
publication date: 2011-01-18T00:00:00Z
review text: The author applies the Galerkin method in order to prove a maximal regularity result for the following abstract gradient system \[ \begin{cases} u'(t)+\nabla_g E(u(t))=f(t)\quad \text{for a.a.}\;t\in[0,T],\\ u(0)=u_0. \end{cases} \] Here, \(E: V\to\mathbb R\) is a continuously differentiable function over a real Banach space \(V\) densely and compactly embedded into a real Hilbert space \(H,\) \(\nabla_g E\) stands for the gradient of \(E\) with respect to some metric \(g,\) \(f\in L^2(0,T;H)\) and \(u_0\in V.\) The abstract result is applied to nonlinear diffusion equations and to nondegenerate quasilinear parabolic equations with nonlocal coefficients.
reviewed by: Dian K. Palagachev
Mathematics Subject Classification ID: 47E05
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35G10
Mathematics Subject Classification ID: 47A60
Mathematics Subject Classification ID: 47J35
zbMATH DE Number: 5838454
zbMATH Keywords: gradient systems
zbMATH Keywords: nonautonomous nonlinear diffusion
zbMATH Keywords: maximal regularity
MaRDI profile type: Publication
full work available at URL: j.jde.2010.09.009
OpenAlex ID: W2059359538
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DOI: 10.1016/J.JDE.2010.09.009
description: scientific article; zbMATH DE number 5838454