Related papers: Hyperbolic Model Reduction for Kinetic Equations

We prove local existence and uniqueness of the Cauchy problem for a large class of tensorial second order linear hyperbolic partial differential equations with coefficients of low regularity in a suitable class of generalized functions.

This paper is devoted to strictly hyperbolic systems and equations with non-smooth coefficients. Below a certain level of smoothness, distributional solutions may fail to exist. We construct generalised solutions in the Colombeau algebra of…

We analyze the Cauchy problem for symmetric hyperbolic equations with a time singularity of Fuchsian type and establish a global existence theory along with decay estimates for evolutions towards the singular time under a small initial data…

The Boltzmann equation has been a driving force behind significant mathematical research over the years. Its challenging theoretical complexity, combined with a wide variety of current scientific and technological problems that require…

We study the Cauchy problem for the Laplace equation in a cylindrical domain with data on a part of it's boundary which is a cross-section of the cylinder. On reducing the problem to the Cauchy problem for the wave equation in a complex…

The Boltzmann equation, a fundamental equation in kinetic theory, serves as a bridge between microscopic particle dynamics and macroscopic continuum mechanics. However, deriving closed macroscopic moment systems from the Boltzmann equation…

We present a new entropy-based moment method for the velocity discretization of kinetic equations. This method is based on a regularization of the optimization problem defining the original entropy-based moment method, and this gives the…

Extended Thermodynamics is the natural framework in which to study the physics of fluids, because it leads to symmetric hyperbolic systems of field laws, thus assuming important properties such as finite propagation speeds of shock waves…

It is shown that early suggested derivation of the Boltzmann kinetic equation for dilute hard sphere gas from the time-reversible BBGKY equations is incorrect since in fact a priori substitutes for them definite irreversible equations.…

Starting from a non-local version of the Prigogine-Herman traffic model, we derive a natural hierarchy of kinetic discrete velocity models for traffic flow consisting of systems of quasi-linear hyperbolic equations with relaxation terms.…

In this paper, we study the Gevrey regularity of weak solutions for a class of linear and semi-linear kinetic equations, which are the linear model of spatially inhomogeneous Boltzmann equations without an angular cutoff.

We study a quantum Boltzmann-Condensation system that describes the evolution of the interaction between a well formed Bose-Einstein condensate and the quasi-particles cloud. The kinetic model is valid for a dilute regime at which the…

It is studied the Cauchy problem for the equations of Burgers' type but with bounded dissipation flux. Such equations degenerate to hyperbolic ones as the velocity gradient tends to infinity. Thus the discontinuous solutions are permitted.…

An Euler-type hyperbolic-parabolic system of chemotactic aggregation describing the vascular network formation is investigated in the critical regularity setting. For small initial data around a constant equilibrium state, the…

Geophysical flow simulations using hyperbolic shallow water moment equations require an efficient discretization of a potentially large system of PDEs, the so-called moment system. This calls for tailored model order reduction techniques…

Hyperbolic formulations of the equations of motion are essential technique for proving the well-posedness of the Cauchy problem of a system, and are also helpful for implementing stable long time evolution in numerical applications. We,…

In the present manuscript we consider the Boltzmann equation that models a polyatomic gas by introducing one additional continuous variable, referred to as microscopic internal energy. We establish existence and uniqueness theory in the…

Hyperbolic conservation laws posed on manifolds arise in many applications to geophysical flows and general relativity. Recent work by the author and his collaborators attempts to set the foundations for a study of weak solutions defined on…

In this paper, we consider the well-posedness of the Cauchy problem for a physical model of the extrusion process, which is described by two systems of conservation laws with a free boundary. By suitable change of coordinates and fixed…

Maxwell models for nonlinear kinetic equations have many applications in physics, dynamics of granular gases, economy, etc. In the present manuscript we consider such models from a very general point of view, including those with arbitrary…