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Optimal Entropy-Transport problems and a new Hellinger–Kantorovich distance between positive measures
We develop a full theory for the new class of Optimal Entropy-Transport problems between nonnegative and finite Radon measures in general topological spaces. These problems arise quite naturally byExpand
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Optimal Transport in Competition with Reaction: The Hellinger-Kantorovich Distance and Geodesic Curves
TLDR
We discuss a new notion of distance on the space of finite and nonnegative measures on $\Omega \subset {\mathbb R}^d$, which we call the Hellinger--Kantorovich distance. Expand
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Gradient structures and geodesic convexity for reaction–diffusion systems
  • M. Liero, A. Mielke
  • Mathematics, Medicine
  • Philosophical Transactions of the Royal Society A…
  • 1 September 2012
We consider systems of reaction–diffusion equations as gradient systems with respect to an entropy functional and a dissipation metric given in terms of a so-called Onsager operator, which is a sumExpand
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On gradient structures for Markov chains and the passage to Wasserstein gradient flows
  • K. Disser, M. Liero
  • Mathematics, Computer Science
  • Networks Heterog. Media
  • 30 December 2013
TLDR
We show that simple finite-volume discretizations of the linear Fokker-Planck equation exhibit the recently established entropic gradient-flow structure for reversible Markov chains. Expand
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Rate independent Kurzweil processes
The Kurzweil integral technique is applied to a class of rate independent processes with convex energy and discontinuous inputs. We prove existence, uniqueness, and continuous data dependence ofExpand
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On microscopic origins of generalized gradient structures
Classical gradient systems have a linear relation between rates and driving forces. In generalized gradient systems we allow for arbitrary relations derived from general non-quadratic dissipationExpand
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Homogenization of Cahn – Hilliard-type equations via evolutionary Γ-convergence
In this paper we discuss two approaches to evolutionary Γ-convergence of gradient systems in Hilbert spaces. The formulation of the gradient system is based on two functionals, namely the energyExpand
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A New Minimum Principle for Lagrangian Mechanics
TLDR
We present a novel variational view at Lagrangian mechanics based on the minimization of weighted inertia-energy functionals on trajectories. Expand
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Point contacts at the copper-indium-gallium-selenide interface—A theoretical outlook
For a long time, it has been assumed that recombination in the space-charge region of copper-indium-gallium-selenide (CIGS) is dominant, at least in high efficiency solar cells with low band gap. TheExpand
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AN EVOLUTIONARY ELASTOPLASTIC PLATE MODEL DERIVED VIA Γ-CONVERGENCE
This paper is devoted to dimension reduction for linearized elastoplasticity in the rate-independent case. The reference configuration of the three-dimensional elastoplastic body has aExpand
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