Variational formulation and structural stability of monotone equations

DOI10.1007/s00526-012-0519-yzbMath1304.47073OpenAlexW1973011532MaRDI QIDQ1949409

Augusto Visintin

Publication date: 7 May 2013

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-012-0519-y

zbMATH Keywords

structural stabilitymonotone operatorlong memorygamma-convergencemonotone inclusionrepresentative functionvariational representationmonotone flow

Mathematics Subject Classification ID

Variational inequalities (49J40) Monotone operators and generalizations (47H05) Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Set-valued operators (47H04) Existence of solutions for minimax problems (49J35) Methods involving semicontinuity and convergence; relaxation (49J45) Evolution inclusions (34G25) Variational problems in infinite-dimensional spaces (58E99) Nonlinear evolution equations (47J35) Variational and other types of inclusions (47J22)

Related Items (19)

A gradient system with a wiggly energy and relaxed EDP-convergence ⋮ A variational approach to nonlinear stochastic differential equations with linear multiplicative noise ⋮ An additive subfamily of enlargements of a maximally monotone operator ⋮ Enlargements: a bridge between maximal monotonicity and convexity ⋮ Stochastic homogenization of maximal monotone relations and applications ⋮ An extension of the Fitzpatrick theory ⋮ \( \Gamma \)-compactness and \(\Gamma \)-stability of maximal monotone flows ⋮ Structural Compactness and Stability of Semi-Monotone Flows ⋮ Effective diffusion in thin structures via generalized gradient systems and EDP-convergence ⋮ On the variational representation of monotone operators ⋮ Lipschitz regularity for elliptic equations with random coefficients ⋮ New variational principles for solving extended Dirichlet-Neumann problems ⋮ Generation of balanced viscosity solutions to rate-independent systems via variational convergence ⋮ Visco-energetic solutions to some rate-independent systems in damage, delamination, and plasticity ⋮ Weighted energy-dissipation principle for gradient flows in metric spaces ⋮ \( \Gamma \)-compactness and \( \Gamma \)-stability of the flow of heat-conducting fluids ⋮ Variational approach to homogenization of doubly-nonlinear flow in a periodic structure ⋮ Weak structural stability of pseudo-monotone equations ⋮ \( \Gamma \)-stability of maximal monotone processes

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