Related papers: One Dimensional Hyperbolic Conservation Laws: Past…
In this paper, we discuss the notion of discrete conservation for hyperbolic conservation laws. We introduce what we call a fluctuation splitting schemes (or residual distribution, also RDS) and show on several examples how this cal lead to…
A quadratic interaction potential $t \mapsto \Upsilon(t)$ for hyperbolic systems of conservation laws is constructed, whose value $\Upsilon(\bar t)$ at time $\bar t$ depends only on the present and the future profiles of the solution and…
This thesis deals with the formulation and analysis of two systems of conservation laws defined on two complementary intervals and coupled by some moving interface as a single infinite-dimensional port-Hamiltonian system. This approach may…
This text is about geometric structures imposed by robust dynamical behaviour. We explain recent results towards the classification of partially hyperbolic systems in dimension 3 using the theory of foliations and its interaction with…
Proposed is system of consistent mathematical models describing physical laws of a system of energy emitting bodies in dynamics, relativity and nuclear physics. It is shown the use of developed models for the description of systems,…
This paper presents a backstepping approach for the boundary control of first-order hyperbolic equations with spatially varying coefficients posed on domains of arbitrary dimension. The method is based on a change of variables induced by…
The aim of these notes is to connect the theory of hyperbolic and relatively hyperbolic groups to the theory of manifolds and Kleinian groups. We survey some of the extensive work that has been done in the field, and explain many examples.…
Conservation laws are discussed in conjunction with quantum-mechanical indeterminacies of the corresponding observables. The considered examples show that the connections between energy and its indeterminacy may be quite intricate. The…
Entropy solutions have been widely accepted as the suitable solution framework for systems of conservation laws in several space dimensions. However, recent results in \cite{CDL1,CDL2} have demonstrated that entropy solutions may not be…
A number of physical phenomena are described by nonlinear hyperbolic equations. Presence of discontinuous solutions motivates the necessity of development of reliable numerical methods based on the fundamental mathematical properties of…
Freeze-out of particles in relativistic hydrodynamics is considered across a 3-dimensional space-time hypersurface. The conservation laws for time-like parts of the freeze-out hypersurface require different values of temperature, baryonic…
In a recent paper, PNAS, 118, e1921529118 (2021), it was argued that while the standard definition of conservation laws in quantum mechanics, which is of a statistical character, is perfectly valid, it misses essential features of nature…
This article studies a hyperbolic conservation law that models a highly re-entrant manufacturing system as encountered in semi-conductor production. Characteristic features are the nonlocal character of the velocity and that the influx and…
We present the hydrodynamics of fluids in three spatial dimensions with helical symmetry, wherein only a linear combination of a rotation and translation is conserved in one of the three directions. The hydrodynamic degrees of freedom…
A new representation of the Einstein evolution equations is presented that is first order, linearly degenerate, and symmetric hyperbolic. This new system uses the generalized harmonic method to specify the coordinates, and exponentially…
We study a model of assisted diffusion of hard-core particles on a line. The model shows strongly ergodicity breaking : configuration space breaks up into an exponentially large number of disconnected sectors. We determine this…
A detailed analysis of the coupled relativistic kinetic equations for two domains separated by a hypersurface having both space- and time-like parts is presented. Integrating the derived set of transport equations, we obtain the correct…
This article critically reviews the proposal for addressing the cosmological constant problem within the framework of supersymmetric large extra dimensions (SLED), as recently proposed in hep-th/0304256. After a brief restatement of the…
We derive entropy conserving and entropy dissipative overlapping domain formulations for systems of nonlinear hyperbolic equations in conservation form, such as would be approximated by overset mesh methods. The entropy conserving…
Motivated by the need to control the exponential growth of constraint violations in numerical solutions of the Einstein evolution equations, two methods are studied here for controlling this growth in general hyperbolic evolution systems.…