Balanced viscosity (BV) solutions to infinite-dimensional rate-independent systems

DOI10.4171/JEMS/639zbMath1357.35007arXiv1309.6291WikidataQ59901703 ScholiaQ59901703MaRDI QIDQ303837

Giuseppe Savaré, Riccarda Rossi, Alexander Mielke

Publication date: 22 August 2016

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1309.6291

zbMATH Keywords

vanishing viscosityexistence resultstime discretizationenergetic solutionsBV solutionschain-rule inequalitysuperlinear vanishing-viscosity dissipation

Mathematics Subject Classification ID

Variational methods applied to PDEs (35A15) Ordinary differential inclusions (34A60) Viscosity solutions to PDEs (35D40)

Related Items (45)

Finite plasticity in \(P^\top P\). I: Constitutive model ⋮ A doubly monotone flow for constant width bodies in ℝ³ ⋮ Rate-Independent Systems and Their Viscous Regularizations: Analysis, Simulation, and Optimal Control ⋮ Unnamed Item ⋮ Energetic solutions for the coupling of associative plasticity with damage in geomaterials ⋮ Two-speed solutions to non-convex rate-independent systems ⋮ Singular vanishing-viscosity limits of gradient flows: the finite-dimensional case ⋮ Balanced-viscosity solutions to infinite-dimensional multi-rate systems ⋮ Optimal Control of a Rate-Independent System Constrained to Parametrized Balanced Viscosity Solutions ⋮ From visco to perfect plasticity in thermoviscoelastic materials ⋮ The notions of inertial balanced viscosity and inertial virtual viscosity solution for rate-independent systems ⋮ Convergence analysis of time-discretisation schemes for rate-independent systems ⋮ A gradient system with a wiggly energy and relaxed EDP-convergence ⋮ Irreversibility and alternate minimization in phase field fracture: a viscosity approach ⋮ Energetic formulation for rate-independent processes: remarks on discontinuous evolutions with a simple example ⋮ Vanishing‐viscosity solutions to a rate‐independent two‐field gradient damage model ⋮ Viscous corrections of the time incremental minimization scheme and visco-energetic solutions to rate-independent evolution problems ⋮ Quasistatic evolution in non-associative plasticity revisited ⋮ Singular limits of a coupled elasto-plastic damage system as viscosity and hardening vanish ⋮ A Priori Error Analysis of Local Incremental Minimization Schemes for Rate-Independent Evolutions ⋮ A unilateral \(L^2\)-gradient flow and its quasi-static limit in phase-field fracture by an alternate minimizing movement ⋮ Balanced viscosity solutions to a rate-independent system for damage ⋮ Variational methods for evolution. Abstracts from the workshop held November 12--18, 2017 ⋮ Finite element discretization of local minimization schemes for rate-independent evolutions ⋮ Existence, Energy Identity, and Higher Time Regularity of Solutions to a Dynamic Viscoelastic Cohesive Interface Model ⋮ Quadratic and rate-independent limits for a large-deviations functional ⋮ Gradient flows of time-dependent functionals in metric spaces and applications to PDEs ⋮ Existence of parameterized BV-solutions for rate-independent systems with discontinuous loads ⋮ Quasistatic crack growth based on viscous approximation: a model with branching and kinking ⋮ An existence result and evolutionary \(\varGamma \)-convergence for perturbed gradient systems ⋮ Fatigue effects in elastic materials with variational damage models: a vanishing viscosity approach ⋮ Coupling Rate-Independent and Rate-Dependent Processes: Existence Results ⋮ Visco-energetic solutions to one-dimensional rate-independent problems ⋮ Multiscale analysis of singularly perturbed finite dimensional gradient flows: the minimizing movement approach ⋮ BV solutions constructed using the epsilon-neighborhood method ⋮ Generation of balanced viscosity solutions to rate-independent systems via variational convergence ⋮ A vanishing-inertia analysis for finite-dimensional rate-independent systems with nonautonomous dissipation and an application to soft crawlers ⋮ Analysis of staggered evolutions for nonlinear energies in phase field fracture ⋮ Visco-energetic solutions to some rate-independent systems in damage, delamination, and plasticity ⋮ Jump processes as generalized gradient flows ⋮ A minimizing Movement approach to a class of scalar reaction–diffusion equations ⋮ Balanced Viscosity Solutions to a Rate-Independent Coupled Elasto-plastic Damage System ⋮ Crack growth by vanishing viscosity in planar elasticity ⋮ Convergence analysis of a local stationarity scheme for rate-independent systems ⋮ Viscous approximation of quasistatic evolutions for a coupled elastoplastic-damage model

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Quasistatic evolution for Cam-Clay plasticity: properties of the viscosity solution
• Quadratic and rate-independent limits for a large-deviations functional
• Quasistatic evolution for Cam-Clay plasticity: a weak formulation via viscoplastic regularization and time rescaling
• Global existence for rate-independent gradient plasticity at finite strain
• Modeling solutions with jumps for rate-independent systems on metric spaces
• Crack growth in polyconvex materials
• On some doubly nonlinear evolution equations in Banach spaces
• Materials with memory. Initial-boundary value problems for constitutive equations with internal variables
• Quasistatic crack growth in nonlinear elasticity
• On rate-independent hysteresis models
• Variational convergence of gradient flows and rate-independent evolutions in metric spaces
• Nonsmooth analysis of doubly nonlinear evolution equations
• A characterization of energetic and \(BV\) solutions to one-dimensional rate-independent systems
• Quasi-static Evolution in Nonassociative Plasticity: The Cap Model
• Differential, Energetic, and Metric Formulations for Rate-Independent Processes
• BV solutions and viscosity approximations of rate-independent systems
• Gradient flows of non convex functionals in Hilbert spaces and applications
• On A Class Of Doubly Nonlinear Evolution Equations
• ON THE INVISCID LIMIT OF A MODEL FOR CRACK PROPAGATION
• A VANISHING VISCOSITY APPROACH TO A RATE-INDEPENDENT DAMAGE MODEL
• RATE-INDEPENDENT DAMAGE PROCESSES IN NONLINEAR ELASTICITY
• On the vanishing-viscosity limit in parabolic systems with rate-independent dissipation terms
• Convex Analysis

This page was built for publication: Balanced viscosity (BV) solutions to infinite-dimensional rate-independent systems