相关论文: New dimensional bounds for a branched transport pr…
We construct the Einstein-axions AdS black hole from Born-Infeld electrodynamics. Various DC transport coefficients of the dual boundary theory are computed. The DC electric conductivity depends on the temperature, which is a novel property…
The main purpose of this paper is to investigate the behaviour of fractional integral operators associated to a measure on a metric space satisfying just a mild growth condition, namely that the measure of each ball is controlled by a fixed…
There has been significant progress recently in our understanding of the stationary measures of the exclusion process on $Z$. The corresponding situation in higher dimensions remains largely a mystery. In this paper we give necessary and…
This paper deals with collisionless transport equations in bounded open domains $\Omega \subset \R^{d}$ $(d\geq 2)$ with $\mathcal{C}^{1}$ boundary $\partial \Omega $, orthogonally invariant velocity measure $\bm{m}(\d v)$ with support…
This paper concerns the reconstruction of the absorption and scattering parameters in a time-dependent linear transport equation from knowledge of angularly averaged measurements performed at the boundary of a domain of interest. We show…
In this article the correctness of al inear inverse problem with semi-nonlocal boundary conditions for a three-dimensional equation in a parallelepiped is considered. The equation itself is a fourth order mixed type equation of the second…
This work deals with a numerical method for solving a mean-field type control problem with congestion. It is the continuation of an article by the same authors, in which suitably defined weak solutions of the system of partial differential…
We develop a new framework for branched transport between probability measures which are allowed to vary in time. This framework can be used to model problems where the underlying transportation network displays a branched structure, but…
Sufficient conditions for the invariance of evolution problems governed by perturbations of (possibly nonlinear) $m$-accretive operators are provided. The conditions for the invariance with respect to sublevel sets of a constraint…
We give a simple criterion on the set of probability tangent measures $\mathrm{Tan}(\mu,x)$ of a positive Radon measure $\mu$, which yields lower bounds on the Hausdorff dimension of $\mu$. As an application, we give an elementary and…
The axion Weak Gravity Conjecture implies that when parametrically increasing the axion decay constants, instanton corrections become increasingly important. We provide strong evidence for the validity of this conjecture by studying the…
This paper discusses the issue of non-uniqueness of the permeability of a porous medium with a random structure. The permeability range for 12,000 realizations of a random porous structure is examined using a recently-developed modelling…
In this article we study the asymptotic behavior of incompressible, ideal, time-dependent two dimensional flow in the exterior of a single smooth obstacle when the size of the obstacle becomes very small. Our main purpose is to identify the…
This paper addresses input-to-state stability (ISS) properties with respect to boundary and in-domain disturbances for a class of semi-linear partial differential equations (PDEs) subject to Dirichlet boundary conditions. The developed…
Accurate transport algorithms are crucial for computational fluid dynamics and more accurate and efficient schemes are always in development. One dimensional limiting is commonly employed to suppress nonphysical oscillations. However, the…
Second-order superintegrable systems in dimensions two and three are essentially classified. With increasing dimension, however, the non-linear partial differential equations employed in current methods become unmanageable. Here we propose…
We study forward and inverse problems for a semilinear radiative transport model where the absorption coefficient depends on the angular average of the transport solution. Our first result is the well-posedness theory for the transport…
We prove the existence of generalised solutions of the Monge-Kantorovich equations with fractional $s$-gradient constraint, $0<s<1$, associated to a general, possibly degenerate, linear fractional operator of the type, \begin{equation*}…
We analyse a stationary problem for the two dimensional model of morphogen transport introduced by Hufnagel et al. The model consists of one linear elliptic PDE posed on $(-1,1)\times(0,h)$ which is coupled via a nonlinear boundary…
This paper is concerning the inverse conductive scattering of acoustic waves by a bounded inhomogeneous object with possibly embedded obstacles inside. A new uniqueness theorem is proved that the conductive object is uniquely determined by…