Gradient regularity for widely degenerate elliptic partial differential equations [0.03%]
强退化椭圆型偏微分方程的梯度 регулярность
Michael Strunk
Michael Strunk
In this paper, we investigate the regularity of weak solutions u : Ω → R to elliptic equations of the type div ∇ F ( x , D u ) = f in Ω , whose ellipticity degenerates in a fixed bounded and convex set E &...
Overcoming the curse of dimensionality in the numerical approximation of high-dimensional semilinear elliptic partial differential equations [0.03%]
克服高维半线性椭圆偏微分方程数值逼近中维度诅咒的问题
Christian Beck,Lukas Gonon,Arnulf Jentzen
Christian Beck
Recently, so-called full-history recursive multilevel Picard (MLP) approximation schemes have been introduced and shown to overcome the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equa...
Existence and non-uniqueness of stationary states for the Vlasov-Poisson equation on [Formula: see text] subject to attractive background charges [0.03%]
Vlasov-Poisson方程在[Formula: see text]空间中存在吸引背景荷电情况下平稳态的存在性与非唯一性
Raphael Winter
Raphael Winter
We prove the existence of stationary solutions for the density of an infinitely extended plasma interacting with an arbitrary configuration of background charges. Furthermore, we show that the solution cannot be unique if the total charge o...
Verena Bögelein,Frank Duzaar,Christoph Scheven
Verena Bögelein
In this paper we establish a local higher integrability result for the spatial gradient of weak solutions to doubly nonlinear parabolic systems. The proof is based on a new intrinsic scaling that involves both the solution and its spatial g...
From agent-based models to the macroscopic description of fake-news spread: the role of competence in data-driven applications [0.03%]
基于代理模型的假新闻传播宏观描述及数据驱动应用中的知识作用研究
J Franceschi,L Pareschi,M Zanella
J Franceschi
Fake news spreading, with the aim of manipulating individuals' perceptions of facts, is now recognized as a major problem in many democratic societies. Yet, to date, little has been understood about how fake news spreads on social networks,...
Modal approximation for plasmonic resonators in the time domain: the scalar case [0.03%]
时域中等离子体共振子的模态近似：标量情形
Lorenzo Baldassari,Pierre Millien,Alice L Vanel
Lorenzo Baldassari
We study the electromagnetic field scattered by a metallic nanoparticle with dispersive material parameters in a resonant regime. We consider the particle placed in a homogeneous medium in a low-frequency regime. We define modes for the non...
Runge-Kutta approximation for [Formula: see text] -semigroups in the graph norm with applications to time domain boundary integral equations [0.03%]
图范数中[Runge--Kutta](http://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods)对-[Formula: see text]-半群的逼近及其在时域边界积分方程中的应用
Alexander Rieder,Francisco-Javier Sayas,Jens Markus Melenk
Alexander Rieder
We consider the approximation of an abstract evolution problem with inhomogeneous side constraint using A-stable Runge-Kutta methods. We derive a priori estimates in norms other than the underlying Banach space. Most notably, we derive esti...
Helmholtz's decomposition for compressible flows and its application to computational aeroacoustics [0.03%]
可压缩流的亥姆霍兹分解及其在计算航空声学中的应用
Stefan Schoder,Klaus Roppert,Manfred Kaltenbacher
Stefan Schoder
The Helmholtz decomposition, a fundamental theorem in vector analysis, separates a given vector field into an irrotational (longitudinal, compressible) and a solenoidal (transverse, vortical) part. The main challenge of this decomposition i...
Jay Gopalakrishnan,Joachim Schöberl,Christoph Wintersteiger
Jay Gopalakrishnan
We introduce a new class of Runge-Kutta type methods suitable for time stepping to propagate hyperbolic solutions within tent-shaped spacetime regions. Unlike standard Runge-Kutta methods, the new methods yield expected convergence properti...