832 citations
- Max Planck Institute for MathematicsDE454 papers
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8 papers · 2 filters
Sharp a-contraction estimates for small extremal shocks
William Golding, Sam Krupa, Alexis Vasseur
In this paper, we study the -contraction property of small extremal shocks for 1-d systems of hyperbolic conservation laws endowed with a single convex entropy, when subjected t…
Uniqueness and weak-BV stability for conservation laws
Geng Chen, Sam G. Krupa, Alexis F. Vasseur
Let a 1-d system of hyperbolic conservation laws, with two unknowns, be endowed with a convex entropy. We consider the family of small functions which are global solutions of…
On a probabilistic model for martensitic avalanches incorporating mechanical compatibility
Francesco Della Porta, Angkana Rüland, Jamie M Taylor +1
Building on the work in \cite{BCH15,CH18,TIVP17}, in this article we propose and study a simple, geometrically constrained, probabilistic algorithm geared towards capturing some as…
Variational approach to regularity of optimal transport maps: general cost functions
Felix Otto, Maxime Prod'homme, Tobias Ried
We extend the variational approach to regularity for optimal transport maps initiated by Goldman and the first author to the case of general cost functions. Our main result is an $…
Global existence and convergence of a flow to Kazdan-Warner equation with non-negative prescribed function
Linlin Sun, Jingyong Zhu
We consider an evolution problem associated to the Kazdan-Warner equation on a closed Riemann surface \begin{align*} -Δ_{g}u=8π\left(\frac{he^{u}}{\int_Σhe^{u}{\rm d}μ_{g}}…
Uniform energy distribution in a pattern-forming system of surface charges
Katarina Bellova, Antoine Julia, Felix Otto
We consider a variational model for a charge density on a (hyper)plane, with a short-range attraction coming from the interfacial energy and a long-range repulsion c…