相关论文: Continuous-time link-based kinematic wave model: f…

In a series of previous works (arXiv:2104.11204, arXiv:2110.04565, arXiv:2301.07063), we gave a rigorous derivation of the homogeneous wave kinetic equation (WKE) up to small multiples of the kinetic timescale, which corresponds to short…

Despite the fact that our physical observations can often be described by derived physical laws, such as the wave equation, in many cases, we observe data that do not match the laws or have not been described physically yet. Therefore…

We study the initial value problem for a kind of Euler equation with a source term. Our main result is the existence of a globally-in-time weak solution whose total variation is bounded on the the domain of definition, allowing the…

This paper is concerned with the existence of the simultaneous route-and-departure choice dynamic user equilibrium (SRDC-DUE) in continuous time, first formulated as an infinite-dimensional variational inequality in Friesz et al. (1993). In…

We prove the existence and uniqueness, for wave speeds sufficiently large, of monotone traveling wave solutions connecting stable to unstable spatial equilibria for a class of $N$-dimensional lattice differential equations with…

Absence of sufficiently high-quality data often poses a key challenge in data-driven modeling of high-dimensional spatio-temporal dynamical systems. Koopman Autoencoders (KAEs) harness the expressivity of deep neural networks (DNNs), the…

In this paper we propose local and global existence results for the solution of systems characterized by the coupling of ODEs and PDEs. The coexistence of distinct mathematical formalisms represents the main feature of hybrid approaches, in…

While synchronized states, and the dynamical pathways through which they emerge, are often regarded as the paradigm to understand the dynamics of information spreading on undirected networks of nonlinear dynamical systems, when we consider…

The main motivation of this work is to assess the validity of a LWR traffic flow model to model measurements obtained from trajectory data, and propose extensions of this model to improve it. A formulation for a discrete dynamical system is…

Fundamental to many transportation network studies, traffic flow models can be used to describe traffic dynamics determined by drivers' car-following, lane-changing, merging, and diverging behaviors. In this study, we develop a…

In recent years, kinetic equations have been used to model many social phenomena. A key feature of these models is that transition rate kernels involve Dirac delta functions, which capture sudden, discontinuous state changes. Here, we study…

Finding extended hydrodynamics equations valid from the dense gas region to the rarefied gas region remains a great challenge. The key to success is to obtain accurate constitutive relations for stress and heat flux. Data-driven models…

We consider the nonlinear Klein Gordon Maxwell system on four dimensional Minkowski space-time. For appropriate nonlinearities the system admits soliton solutions which are gauge invariant generalizations of the non-topological solitons…

In this work, we consider the so-called correlated random walk system (also known as correlated motion or persistent motion system), used in biological modelling, among other fields, such as chromatography. This is a linear system which can…

We study the dynamics of periodic wave trains in reaction-diffusion systems on the real line under large, fully nonlocalized modulations. We prove that solutions with nearby initial data converge, at an enhanced diffusive rate, to a…

In this paper we consider a system coupling a wave equation with a heat equation through its boundary conditions. The existence of a small parameter in the heat equation, as a factor multiplying the time derivative, implies the existence of…

This paper is concerned with dynamic user equilibrium with elastic travel demand (E-DUE) when the trip demand matrix is determined endogenously. We present an infinite-dimensional variational inequality (VI) formulation that is equivalent…

In designing efficient feedback control laws for fluid flow, the modern control theory can serve as a powerful tool if the model can be represented by a linear ordinary differential equation (ODE). However, it is generally difficult to find…

In this paper, we introduce a data-driven modeling approach for dynamics problems with latent variables. The state-space of the proposed model includes artificial latent variables, in addition to observed variables that can be fitted to a…

User equilibrium is a central concept for studying transportation networks, and one can view it as the result of a dynamical process of drivers' route choice behavior. In this paper, based on a definition of O-D First-In-First-Out…