A Generalization of Onsager’s Reciprocity Relations to Gradient Flows with Nonlinear Mobility ⬇️

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A RATE-INDEPENDENT MODEL FOR THE ISOTHERMAL QUASI-STATIC EVOLUTION OF SHAPE-MEMORY MATERIALS

A Rate-Independent Approach to the Delamination Problem

A Rate-Independent Model for Inelastic Behavior of Shape-Memory Alloys

A Variational Formulation of¶Rate-Independent Phase Transformations¶Using an Extremum Principle

A class of minimum principles for characterizing the trajectories and the relaxation of dissipative systems

A complete-damage problem at small strains

A discrete variational principle for rate-independent evolution

A gradient structure for reaction–diffusion systems and for energy-drift-diffusion systems

A gradient structure for systems coupling reaction–diffusion effects in bulk and interfaces

A model for temperature-induced phase transformations in finite-strain elasticity

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A model for the evolution of laminates in finite-strain elastoplasticity

A new identity for the surface-impedance matrix and its application to the determination of surface-wave speeds

scientific article published in 2002

A proof of the Benjamin-Feir instability

A spatial dynamics approach to three-dimensional gravity-capillary steady water waves

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AN EVOLUTIONARY ELASTOPLASTIC PLATE MODEL DERIVED VIA Γ-CONVERGENCE

An Approach to Nonlinear Viscoelasticity via Metric Gradient Flows

An Entropic Gradient Structure for Lindblad Equations and Couplings of Quantum Systems to Macroscopic Models ⬇️

article published in 2017

An energetic material model for time-dependent ferroelectric behaviour: existence and uniqueness

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Analysis and Numerics for Rate-Independent Processes

Attractors for modulation equations on unbounded domains-existence and comparison

BV solutions and viscosity approximations of rate-independent systems

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

Balanced-Viscosity solutions for multi-rate systems

Bifurcation of Homoclinic Orbits to a Saddle-Focus in Reversible Systems with SO(2)-Symmetry

article published in 1999

Bifurcations of Poiseuille flow between parallel plates: Three-dimensional solutions with large spanwise wavelength

Bounds for the solutions of the complex Ginzburg-Landau equation in terms of the dispersion parameters

Calculation of ultrashort pulse propagation based on rational approximations for medium dispersion

Complete damage in elastic and viscoelastic media and its energetics

Convergence of solutions of kinetic variational inequalities in the rate-independent quasi-static limit

Convergence to Equilibrium in Energy-Reaction–Diffusion Systems Using Vector-Valued Functional Inequalities

Crack growth in polyconvex materials

Damage of nonlinearly elastic materials at small strain - Existence and regularity results -

Deriving Effective Models for Multiscale Systems via Evolutionary $$\varGamma $$ Γ -Convergence

Deriving amplitude equations via evolutionary $\Gamma$-convergence

Deriving new evolution equations for microstructures via relaxation of variational incremental problems

Differential, Energetic, and Metric Formulations for Rate-Independent Processes

Diffusive Mixing of Stable States in the Ginzburg-Landau Equation

Dispersive stability of infinite-dimensional Hamiltonian systems on lattices

Dynamical Properties of Spatially Non-Decaying 2D Navier?Stokes Flows with Kolmogorov Forcing in an Infinite Strip

EXISTENCE AND UNIQUENESS RESULTS FOR A CLASS OF RATE-INDEPENDENT HYSTERESIS PROBLEMS

Emergence of rate-independent dissipation from viscous systems with wiggly energies

Energetic formulation of multiplicative elasto-plasticity using dissipation distances

article by Alexander Mielke published 1 August 2003 in Continuum Mechanics and Thermodynamics

Energy release rate for cracks in finite-strain elasticity

article published in 2008

Errata to “The free energy of mixing for n-variant martensitic phase transformations using quasi-convex analysis”

Error Estimates for Space-Time Discretizations of a Rate-Independent Variational Inequality

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Essential Manifolds for an Elliptic Problem in an Infinite Strip

Existence and approximation for a 3D model of thermally-induced phase transformations in shape-memory alloys

Existence of Minimizers in Incremental Elasto-Plasticity with Finite Strains

article by Alexander Mielke published January 2004 in SIAM Journal on Mathematical Analysis

Existence results for a class of rate-independent material models with nonconvex elastic energies

Existence results for a contact problem with varying friction coefficient and nonlinear forces

Existence results for energetic models for rate-independent systems

Existence, numerical convergence and evolutionary relaxation for a rate-independent phase-transformation model.

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Formulation of thermoelastic dissipative material behavior using GENERIC

Free Energy, Free Entropy, and a Gradient Structure for Thermoplasticity

From Damage to Delamination in Nonlinearly Elastic Materials at Small Strains

From Discrete Visco-Elasticity to Continuum Rate-Independent Plasticity: Rigorous Results

article by Alexander Mielke & Lev Truskinovsky published 16 September 2011 in Archive for Rational Mechanics and Analysis

Generalized Prandtl–Ishlinskii operators arising from homogenization and dimension reduction

Geodesic convexity of the relative entropy in reversible Markov chains

Global Existence Results for Viscoplasticity at Finite Strain

Global Existence for Rate-Independent Gradient Plasticity at Finite Strain

article by Andreas Mainik & Alexander Mielke published 6 November 2008 in Journal of Nonlinear Science

Global existence and uniqueness for an optical fibre laser model

Global existence for a nonlocal and nonlinear Fokker–Planck equation

Gradient structures and geodesic convexity for reaction-diffusion systems.

scientific article published on 18 November 2013

HOMOGENIZATION OF ELASTIC WAVES IN FLUID-SATURATED POROUS MEDIA USING THE BIOT MODEL

Infinite-Dimensional Hyperbolic Sets and Spatio-Temporal Chaos in Reaction Diffusion Systems in $${\mathbb{R}^{n}}$$

Infinite-dimensional trajectory attractors of elliptic boundary-value problems in cylindrical domains

article published in 2002

Instability and Stability of Rolls in the Swift-Hohenberg Equation

Instability of Spatially — Periodic States for a Family of Semilinear PDE's on an Infinite Strip

Interaction of modulated pulses in the nonlinear Schrödinger equation with periodic potential

Lagrangian and Hamiltonian two-scale reduction

Linearized elasticity as Mosco limit of finite elasticity in the presence of cracks

Linearized plasticity is the evolutionary $\Gamma$-limit of finite plasticity

article by Alexander Mielke & Ulisse Stefanelli published 2013 in Journal of the European Mathematical Society

Local control of globally competing patterns in coupled Swift–Hohenberg equations

scientific article published on 01 April 2018

Lower semicontinuity and existence of minimizers in incremental finite-strain elastoplasticity

Macroscopic Behavior of Microscopic Oscillations in Harmonic Lattices via Wigner-Husimi Transforms

Mathematical analysis of sideband instabilities with application to rayleigh-bénard convection

Micro–macro transition in the atomic chain via Whitham's modulation equation

Modeling and Analytical Study for Ferroelectric Materials

Modeling solutions with jumps for rate-independent systems on metric spaces

article published in 2009

Modelling of Microstructure and its Evolution in Shape-Memory-Alloy Single-Crystals, in Particular in CuAlNi

article published in 2005

Multi-pulse solutions to the Navier-Stokes problem between parallel plates

Nonlocal modulation equations for viscous-fluid flows in layers and spatially localized perturbations

Nonsmooth analysis of doubly nonlinear evolution equations

Numerical approaches to rate-independent processes and applications in inelasticity

ON THE INVISCID LIMIT OF A MODEL FOR CRACK PROPAGATION

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On Evolutionary $$\varGamma $$ Γ -Convergence for Gradient Systems

On Existence and Approximation for a 3D Model of Thermally Induced Phase Transformations in Shape-Memory Alloys

On Uniform Decay of the Entropy for Reaction–Diffusion Systems

On microscopic origins of generalized gradient structures

On rate independent models for crack propagation

On rate-independent hysteresis models

On the Energy Release Rate in Finite–Strain Elasticity

On the Relation between Gradient Flows and the Large-Deviation Principle, with Applications to Markov Chains and Diffusion

On the energetic stability of solitary water waves

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On the existence of global‐in‐time weak solutions and scaling laws for Kolmogorov's two‐equation model for turbulence

scientific article published in 2022

On the justification of plate theories in linear elasticity theory using exponential decay estimates

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Optimal Transport in Competition with Reaction: The Hellinger--Kantorovich Distance and Geodesic Curves

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Padé approximant for refractive index and nonlocal envelope equations

Passing to the limit in a Wasserstein gradient flow: from diffusion to reaction

RATE-INDEPENDENT DAMAGE PROCESSES IN NONLINEAR ELASTICITY

Rate-independent elastoplasticity at finite strains and its numerical approximation

Relating a Rate-Independent System and a Gradient System for the Case of One-Homogeneous Potentials

scientific article published in 2021

Reverse Approximation of Energetic Solutions to Rate-Independent Processes

Spectrum and amplitude equations for scalar delay-differential equations with large delay

The complex Ginzburg - Landau equation on large and unbounded domains: sharper bounds and attractors

The nonlinear Schrödinger equation as a macroscopic limit for an oscillator chain with cubic nonlinearities

Thermomechanical modeling of energy-reaction-diffusion systems, including bulk-interface interactions

Traveling Fronts in a Reaction–Diffusion Equation with a Memory Term

scientific article published in 2022

Two-Scale Homogenization for Evolutionary Variational Inequalities via the Energetic Formulation

Two-scale homogenization of nonlinear reaction-diffusion systems with slow diffusion

Uniqueness of the Surface-Wave Speed: A Proof That Is Independent of the Stroh Formalism

Variational Convergence of Gradient Flows and Rate-Independent Evolutions in Metric Spaces

Vortex pinning in super-conductivity as a rate-independent process

Weighted energy-dissipation functionals for gradient flows

Γ-limits and relaxations for rate-independent evolutionary problems

article published in 2007