相关论文: Controlling conservation laws I: entropy-entropy f…

Solutions to a class of conservation laws with discontinuous flux are constructed relying on the Crandall-Liggett theory of nonlinear contractive semigroups~\cite{CL}. In particular, the paper studies the existence of backward Euler…

We consider two scalar conservation laws with non-local flux functions, describing traffic flow on roads with rough conditions. In the first model, the velocity of the car depends on an averaged downstream density, while in the second model…

We propose and analyze a one-dimensional multi-species cross-diffusion system with non-zero-flux boundary conditions on a moving domain, motivated by the mod- eling of a Physical Vapor Deposition process. Using the boundedness by entropy…

A class of optimal control problems governed by linear fractional diffusion equation with control constraint is considered. We first establish some results on the existence of strong solution to the state equation and the existence of…

We consider the initial value problem for a scalar conservation law in one space dimension with a single spatial flux discontinuity, the so-called two-flux problem. We prove that a well-known front tracking algorithm has a convergence rate…

Reduced order models of nonlinear conservation laws in fluid dynamics do not typically inherit stability properties of the full order model. We introduce projection-based hyper-reduced models of nonlinear conservation laws which are…

The Reynolds transport theorem occupies a central place in fluid dynamics, providing a generalized integral conservation equation for the transport of any conserved quantity within a fluid, and connected to its corresponding differential…

We investigate coupled stochastic differential equations governing N non-negative continuous random variables that satisfy a conservation principle. In various fields a conservation law requires that a set of fluctuating variables be…

We consider conservation laws with source terms in a bounded domain with Dirichlet boundary conditions. We first prove the existence of a strong trace at the boundary in order to provide a simple formulation of the entropy boundary…

We develop deterministic particle schemes to solve non-local scalar conservation laws with congestion. We show that the discrete approximations converge to the unique entropy solution with an explicit rate of convergence under more general…

We consider a class of stochastic control problems which has been widely used in optimal foraging theory. The state processes have two distinct dynamics, characterized by two pairs of drift and diffusion coefficients, depending on whether…

The direct method of construction of local conservation laws of partial differential equations (PDE) is a systematic method applicable to a wide class of PDE systems [Anco S. and Bluman G., Direct construction method for conservation laws…

Two aspects of a widely used 1D model of blood flow in a single blood vessel are studied by symmetry analysis, where the variables in the model are the blood pressure and the cross-section area of the blood vessel. As one main result, all…

We consider partial differential equations (PDE) of drift-diffusion type in the unit interval, supplemented by either two conservation laws or by a conservation law and a further boundary condition. We treat two different cases: (i) uniform…

We introduce notions of equivalence of conservation laws with respect to Lie symmetry groups for fixed systems of differential equations and with respect to equivalence groups or sets of admissible transformations for classes of such…

We show that the principle of maximum entropy, a variational method appearing in statistical inference, statistical physics, and the analysis of stochastic dynamical systems, admits a geometric description from gauge theory. Using the…

We obtain new transport-entropy inequalities and, as a by-product, new deviation estimates for the laws of two kinds of discrete stochastic approximation schemes. The first one refers to the law of an Euler like discretization scheme of a…

We extend the convergence analysis for methods solving PDE-constrained optimal control problems containing both discrete and continuous control decisions based on relaxation and rounding strategies to the class of first order semilinear…

The reaction diffusion equation arises in physical situations in problems from population growth, genetics and physical sciences. We consider the generalised Fisher equation in cylindrical coordinates from Lie theory stand point. An…

Conservation laws are usually studied in the context of sufficient regularity conditions imposed on the flux function, usually $C^{2}$ and uniform convexity. Some results are proven with the aid of variational methods and a unique minimizer…