Related papers: Measure-valued solutions to nonlocal transport equ…
We prove the well-posedness results, i.e. existence, uniqueness, and stability, of the solutions to a class of nonlocal fully nonlinear parabolic partial differential equations (PDEs), where there is an external time parameter $t$ on top of…
We consider the Laplace equation in a domain of $\mathbb{R}^n$, $n\ge 3$, with a small inclusion of size $\epsilon$. On the boundary of the inclusion we define a nonlinear nonautonomous transmission condition. For $\epsilon$ small enough…
We consider a class of optimal control problems for measure-valued nonlinear transport equations describing traffic flow problems on networks. The objective isto minimise/maximise macroscopic quantities, such as traffic volume or average…
The results of local measurements on some composite quantum systems cannot be reproduced classically. This impossibility, known as quantum nonlocality, represents a milestone in the foundations of quantum theory. Quantum nonlocality is also…
Given two probability measures on sequential data, we investigate the transport problem with time-inconsistent preferences in a discrete-time setting. Motivating examples are nonlinear objectives, state-dependent costs, and regularized…
We introduce the notion of globally updating evolution for a class of weighted networks, in which the weight of a link is characterized by the amount of data packet transport flowing through it. By noting that the packet transport over the…
We use a multi-scale similarity analysis which gives specific relations between the velocity, amplitude and width of localized solutions of nonlinear differential equations, whose exact solutions are generally difficult to obtain.
We provide a well-posedness theory for a class of nonlocal continuity equations on co-evolving graphs. We describe the connection among vertices through an edge weight function and we let it evolve in time, coupling its dynamics with the…
We study a 1D transport equation with nonlocal velocity. First, we prove eventual regularization of the viscous regularization when dissipation is in the supercritical range with non-negative initial data. Next, we will prove global…
We have derived a variational principle that defines the nonequilibrium steady-state transport across a correlated impurity mimicking, e.g., a quantum dot coupled to biased leads. This variational principle has been specialized to a…
In this paper we consider the locally backward self-similar solutions for the Euler system, and focus on the case that the possible nontrivial velocity profiles have non-decaying asymptotics. We derive the meaningful representation formula…
The phenomenological textbook equations for the charge and heat transport are extensively used in a number of fields ranging from semiconductor devices to thermoelectricity. We provide a rigorous derivation of transport equations by solving…
We study traveling wave solutions of the nonlinear variational wave equation. In particular, we show how to obtain global, bounded, weak traveling wave solutions from local, classical ones. The resulting waves consist of monotone and…
Assessment of the degree of boundedness/stability of multidimensional nonlinear systems with time-dependent and nonperiodic coefficients is an important problem in various applied areas which has no adequate resolution yet. Most of the…
We present a multilane traffic model based on balance laws, where the nonlocal source term is used to describe the lane changing rate. The modelling framework includes the consideration of local and nonlocal flux functions. Based on a…
We consider traveling fronts to the nonlocal bistable equation. We do not assume that the Borel-measure is absolutely continuous with respect to the Lebesgue measure. We show that there is a traveling wave solution with monotone profile. In…
We derive a general expression for the streaming term in radiative transport equa- tions and other transport problems when formulated in curvilinear coordinates, emphasizing coordinate systems adapted to the geometry of the domain and the…
We present weighted Sobolev spaces and prove a trace theorem for the spaces. As an application, we discuss non-zero boundary value problems for parabolic equations. The weighted parabolic Sobolev spaces we consider are designed, in…
The paper considers existence of spatially regular solutions for a class of linear Boltzmann transport equations. The related transport problem is an (initial) inflow boundary value problem. This problem is characteristic with variable…
We consider the inverse problem for time-dependent semilinear transport equations. We show that time-independent coefficients of both the linear (absorption or scattering coefficients) and nonlinear terms can be uniquely determined, in a…