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Dynamics as a mechanism preventing the formation of finer and finer microstructure
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What this work says
Outgoing claims: the papers this work cites, builds on, or argues with.
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Metastable patterns in solutions of u t = ϵ 2 u xx − f(u)
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Uniqueness for structural phase transitions in shape memory alloys
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Existence of solutions for a mathematical model of structural phase transitions in shape memory alloys
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Metastable Patterns for the Cahn-Hilliard Equation, Part I
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Metastable Patterns for the Cahn-Hilliard Equation: Part II. Layer Dynamics and Slow Invariant Manifold
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Quasilinear Hyperbolic–Parabolic Equations of One-Dimensional Viscoelasticity
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Dynamics and minimizing sequences
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Infinite-Dimensional Dynamical Systems in Mechanics and Physics
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Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations
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Optimization—Theory and Applications
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Nucleation, Kinetics and Admissibility Criteria for Propagating Phase Boundaries
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On the Problem of Two Wells
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Infinite-Dimensional Dynamical Systems in Mechanics and Physics
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Connecting orbits in scalar reaction diffusion equations
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The approach of solutions of nonlinear diffusion equations to travelling front solutions
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Equilibrium configurations of crystals
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A phase plane discussion of convergence to travelling fronts for nonlinear diffusion
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Phase transitions in one-dimensional nonlinear viscoelasticity: admissibility and stability
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Fine phase mixtures as minimizers of energy
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Characterizations of young measures generated by gradients
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Energy minimization and the formation of microstructure in dynamic anti-plane shear
inferredcites →https://doi.org/10.1007/bf00380505openalex-snapshot
Microstructures with finite surface energy: the two-well problem
inferredcites →https://doi.org/10.1007/bf00386071openalex-snapshot
The nature of configurational forces
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Convergence in gradient-like systems with applications to PDE
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Slow-motion manifolds, dormant instability, and singular perturbations
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Phase transitions of elastic solid materials
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On the dissipation due to wave ringing in nonelliptic elastic materials
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Geometric Theory of Semilinear Parabolic Equations
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The mixed initial-boundary value problem for the equations of nonlinear one-dimensional viscoelasticity
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On the existence of solutions to the equation utt = uxxt + σ(ux)x
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Asymptotic behaviour and changes of phase in one-dimensional nonlinear viscoelasticity
inferredcites →https://doi.org/10.1016/0022-0396(85)90153-6openalex-snapshot
Some infinite-dimensional Morse-Smale systems defined by parabolic partial differential equations
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Connecting orbits in scalar reaction diffusion equations II. The complete solution
inferredcites →https://doi.org/10.1016/0022-0396(91)90096-ropenalex-snapshot
A dynamical system approach to a phase transition problem
inferredcites →https://doi.org/10.1016/0022-0396(91)90163-4openalex-snapshot
Slow motion for the Cahn-Hilliard equation in one space dimension
inferredcites →https://doi.org/10.1016/0167-2789(92)90058-uopenalex-snapshot
Boosted kink-type solitary waves in nonlinear elastic media
inferredcites →https://doi.org/10.1016/0167-2789(93)90236-topenalex-snapshot
Elastic hydrodynamics and dynamical nucleation in first-order strain transitions
inferredcites →https://doi.org/10.1017/s0308210500014177openalex-snapshot
Dynamical modelling of phase transitions by means of viscoelasticity in many dimensions
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Restrictions on microstructure
inferredcites →https://doi.org/10.1017/s0308210500028730openalex-snapshot
A necessary and sufficient condition for nonattainment and formation of microstructure almost everywhere in scalar variational problems
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Young measures and the absence of fine microstructures in a class of phase transitions
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Branching of twins near an austenite—twinned-martensite interface
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Theory of magnetostriction with applications to TbxDy1-xFe2
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The approach of solutions of nonlinear diffusion equations to travelling wave solutions
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Stabilization in a Gradient System with a Conservation Law
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Stable Patterns in a Viscous Diffusion Equation
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Asymptotic Behavior of Dissipative Systems
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Proposed experimental tests of a theory of fine microstructure and the two-well problem
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Interfacial dynamics at a first-order phase transition involving strain: Dynamical twin formation
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Dynamical approach to hysteresis in a bar undergoing a martensitic transformation
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The Dynamics of Nucleation for the Cahn–Hilliard Equation
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On algorithms for non-convex optimization
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Lectures on the Calculus of Variations and Optimal Control Theory
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Lectures on the Calculus of Variations and Optimal Control Theory.
What points at this work
Incoming claims: where this work appears in other papers’ reference lists and arguments.
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Visco‐elasto‐plastic model for martensitic phase transformation in shape‐memory alloys
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Convergence of Solutions to the Equation of Quasi-Static Approximation of Viscoelasticity with Capillarity
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Remarks on Compactness in the Formation of Fine Structures
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Some Open Problems in Elasticity
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Models of Microstructure Evolution in Shape Memory Alloys
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Microstructures, Phase Transitions and Geometry
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Dissipative Evolution of Microstructure in Shape Memory Alloys
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Elements of Elastic Stability Theory
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On the asymptotic behavior of a phase-field model for elastic phase transitions
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Variational models for microstructure and phase transitions
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Asymptotic behavior and dynamic stability of phase mixtures for the equations of Navier–Stokes with nonmonotonic pressure
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Young measure flow as a model for damage
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Convergence of a full discretization for a second-order nonlinear elastodynamic equation in isotropic and anisotropic Orlicz spaces
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Unique Global Solvability for¶Initial-Boundary Value Problems¶in One-Dimensional Nonlinear Thermoviscoelasticity
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The relaxation of non-quasiconvex variational integrals
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Hysteresis and Stick-Slip Motion of Phase Boundaries in Dynamic Models of Phase Transitions
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The computational modeling of nonequilibrium thermodynamics of the martensitic transformations
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Existence of stationary solutions and local minima for 2D models of fine structure dynamics
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Bifurcations in the Regularized Ericksen Bar Model
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Quasistatic Nonlinear Viscoelasticity and Gradient Flows
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Small surface energy, coarse-graining, and selection of microstructure
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On the effect of dissipation in shape-memory alloys
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Dynamics of Phase Transitions and Hysteresis in a Viscoelastic Ericksen's Bar on an Elastic Foundation
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The calculus of variations and materials science
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