Related papers: Uniqueness of a constrained variational problem an…

Bounded variation estimates of Galerkin approximations are established in order to extract an almost everywhere convergent subsequence of Galerkin approximations. As a result we prove existence of weak solutions of initial boundary value…

We study the large deviation function for the empirical measure of diffusing particles at one fixed position. We find that the large deviation function exhibits anomalous system size dependence in systems that satisfy the following…

We discuss the universal scaling laws of order parameter fluctuations in any system in which the second-order critical behavior can be identified. These scaling laws can be derived rigorously for equilibrium systems when combined with the…

Here we investigate 3-dimensional Navier-Stokes Equations in the incompressible case with use of different approach and we prove the uniqueness of the weak solutions for the data from the space, which is dense in usual space of data.…

In this paper we generalize a methodology [T. E. Ouldridge, A. A. Louis, and J. P. K. Doye, J. Phys.: Condens. Matter {\bf 22}, 104102 (2010)] for dealing with the inference of bulk properties from small simulations of self-assembling…

This article is a presentation of specific recent results describing scaling limits of individual-based models. Thanks to them, we wish to relate the time-scales typical of demographic dynamics and natural selection to the parameters of the…

This paper is devoted to the full system of incompressible liquid crystals, as modeled in the Q-tensor framework. The main purpose is to establish the uniqueness of weak solutions in a two dimensional setting, without imposing an extra…

Well posedness is established for a family of equations modelling particle populations undergoing delocalised coagulation, advection, inflow and outflow in a externally specified velocity field. Very general particle types are allowed while…

A bifurcation is a qualitative change in a family of solutions to an equation produced by varying parameters. In contrast to the local bifurcations of dynamical systems that are often related to a change in the number or stability of…

Invariant coordinate selection is an unsupervised multivariate data transformation useful in many contexts such as outlier detection or clustering. It is based on the simultaneous diagonalization of two affine equivariant and positive…

In the present paper, we give some examples of stochastic differential equations which have delicateness in the Markov and strong Markov properties, the uniqueness locally in time and globally in time, and initial conditions. Moreover, we…

We explain how to derive largeness constraints in scalar curvature geometry using some basic splitting results and the potential theory on singular area minimizing hypersurfaces. This includes a variety of results like the non-existence of…

A singularly perturbed problem involving two singular perturbation parameters is discretized using the classical upwinded finite difference scheme on an appropriate piecewise-uniform Shishkin mesh. Scaled discrete derivatives (with scaling…

We obtain sufficient conditions for the uniqueness of solutions to the Cauchy problem for the continuity equation in classes of measures that need not be absolutely continuous.

Scale variation is a deep-rooted problem in object counting, which has not been effectively addressed by existing scale-aware algorithms. An important factor is that they typically involve cooperative learning across multi-resolutions,…

We explain the anomaly of election results between large cities and rural areas in terms of urban scaling in the 1948-2016 US elections and in the 2016 EU referendum of the UK. The scaling curves are all universal and depend on a single…

The Navier-Stokes-Fourier system describing the motion of a compressible, viscous, and heat conducting fluid is known to possess global-in-time weak solutions for any initial data of finite energy. We show that a weak solution coincides…

We study a boundary value elliptic problem having a lower order nonlinear term with subquadratic growth in the gradient of the solution and possibly singular when the solution vanishes. If the singularity is mild enough (and even in the…

In a complete metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we study strict subsets, i.e. sets whose variational capacity with respect to a larger reference set is finite, in the case $p=1$.…

Random embeddings project high-dimensional spaces to low-dimensional ones; they are careful constructions which allow the approximate preservation of key properties, such as the pair-wise distances between points. Often in the field of…