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Mathematics

D-Index
70
Citations
14153
World Ranking
279
National Ranking
17

Overview

Alexander Mielke is affiliated with the Weierstrass Institute for Applied Analysis and Stochastics in Germany. Their research spans multiple domains within mathematics and engineering, with a particular emphasis on applied mathematics and computational theory.

Their publication record includes a variety of recent papers, illustrating involvement in advanced mathematical modeling and analysis topics. Selected recent papers are:

  • Exploring families of energy-dissipation landscapes via tilting: three types of EDP convergence, 2021, Continuum Mechanics and Thermodynamics
  • Modeling of Chemical Reaction Systems with Detailed Balance Using Gradient Structures, 2020, Journal of Statistical Physics
  • EDP-convergence for nonlinear fast-slow reaction systems with detailed balance*, 2021, Nonlinearity
  • On the existence of global-in-time weak solutions and scaling laws for Kolmogorov's two-equation model for turbulence, 2022, ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
  • Global Existence Analysis of Energy-Reaction-Diffusion Systems, 2022, SIAM Journal on Mathematical Analysis

Mielke collaborates frequently with other researchers. Notable co-authors include:

  • Thomas Koprucki
  • Tomáš Roubı́ček
  • Mark A. Peletier
  • Anieza Maltsi
  • Artur Stephan

Their research outputs are often published in venues such as:

  • arXiv (Cornell University)
  • The Spine Journal
  • Archive for Rational Mechanics and Analysis
  • Continuum Mechanics and Thermodynamics
  • SIAM Journal on Mathematical Analysis

Main fields of study for Alexander Mielke include:

  • Mathematics
  • Engineering

Within these fields, Mielke's work delves into the following subfields:

  • Applied Mathematics
  • Computational Theory and Mathematics
  • Statistical and Nonlinear Physics
  • Modeling and Simulation
  • Control and Systems Engineering

The primary topics addressed in their research cover:

  • Advanced Mathematical Modeling in Engineering
  • Mathematical Biology Tumor Growth
  • Stability and Controllability of Differential Equations
  • Advanced Thermodynamics and Statistical Mechanics
  • Geometric Analysis and Curvature Flows
  • Nonlinear Partial Differential Equations
  • Spine and Intervertebral Disc Pathology

Best Publications

  • Non-convex potentials and microstructures in finite-strain plasticity

    Carsten Carstensen;Klaus Hackl;Alexander Mielke

  • On rate-independent hysteresis models

    Alexander Mielke;Florian Theil

  • Optimal Entropy-Transport problems and a new Hellinger–Kantorovich distance between positive measures

    Matthias Liero;Alexander Mielke;Giuseppe Savaré

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

    Alexander Mielke;Florian Theil;Valery I. Levitas

  • Rate-Independent Systems

    Alexander Mielke;Tomáš Roubíček

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

    Alexander Mielke

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

    Gilles Francfort;Alexander Mielke

  • Existence results for energetic models for rate-independent systems

    Andreas Mainik;Alexander Mielke

  • Reduction of quasilinear elliptic equations in cylindrical domains with applications

    Alexander Mielke

  • Rate-Independent Systems: Theory and Application

    Alexander Mielke;Tomáš Roubíček

  • The validity of modulation equations for extended systems with cubic nonlinearities

    Pius Kirrmann;Guido Schneider;Alexander Mielke

  • Attractors for modulation equations on unbounded domains-existence and comparison

    A Mielke;G Schneider

  • Γ-limits and relaxations for rate-independent evolutionary problems

    Alexander Mielke;Tomáš Roubíček;Ulisse Stefanelli

  • Energetic formulation of multiplicative elasto-plasticity using dissipation distances

    A. Mielke

  • Hamiltonian and Lagrangian Flows on Center Manifolds

    Alexander Mielke

  • Geodesic convexity of the relative entropy in reversible Markov chains

    Alexander Mielke

  • RATE-INDEPENDENT DAMAGE PROCESSES IN NONLINEAR ELASTICITY

    Alexander Mielke;Tomáš Roubíček;Tomáš Roubíček

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

    A. Mielke;M. A. Peletier;D. R. M. Renger

  • On the Rate-Independent Limit of Systems with Dry Friction and Small Viscosity

    Messoud A. Efendiev;Alexander Mielke

  • Cascades of homoclinic orbits to, and chaos near, a Hamiltonian saddle-center

    A. Mielke;P. Holmes;O. O'Reilly

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

    Alexander Mielke;Tomás Roubícek

Frequent Co-Authors

Tomáš Roubíček
Tomáš Roubíček Charles University
Giuseppe Savaré
Giuseppe Savaré Bocconi University
Sergey Zelik
Sergey Zelik University of Surrey
Guido Schneider
Guido Schneider University of Stuttgart
Gérard Iooss
Gérard Iooss Université Côte d'Azur
Philip Holmes
Philip Holmes Princeton University
Michael Winkler
Michael Winkler University of Paderborn
Gianni Dal Maso
Gianni Dal Maso International School for Advanced Studies
Peter A. Markowich
Peter A. Markowich King Abdullah University of Science and Technology
Valery I. Levitas
Valery I. Levitas Iowa State University

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