Related papers: Multidimensional Conservation Laws: Overview, Prob…
In the last years measure-valued solutions started to be considered as a relevant notion of solutions if they satisfy the so-called measure-valued -- strong uniqueness principle. This means that they coincide with a strong solution…
The stability of difference schemes for, in general, hyperbolic systems of conservation laws with source terms are studied. The basic approach is to investigate the stability of a non-linear scheme in terms of its cor- responding scheme in…
We propose, study, and compute solutions to a class of optimal control problems for hyperbolic systems of conservation laws and their viscous regularization. We take barotropic compressible Navier--Stokes equations (BNS) as a canonical…
In some models involving nonlinear conservation laws, physical mechanisms exist which prevent the formation of shocks. This gives rise to conservation laws with a constraint on the gradient of the solution. We approach this problem by…
We introduce the concept of energy-variational solutions for hyperbolic conservation laws. Intrinsically, these energy-variational solutions fulfill the weak-strong uniqueness principle and the semi-flow property, and the set of solutions…
We investigate conservation laws of diffusion-convection equations to construct first-order potential systems corresponding to these equations. We do two iterations of the construction procedure, looking, in the second step, for the…
We review the theory of entanglement measures, concentrating mostly on the finite dimensional two-party case. Topics covered include: single-copy and asymptotic entanglement manipulation; the entanglement of formation; the entanglement…
The two-dimensional shallow water equations in Eulerian and Lagrangain coordinates are considered. Lagrangian and Hamiltonian formalism of the equations is given. The transformations mapping the two-dimensional shallow water equations with…
1. The state equation for real gas 2. New state equation for condensed matter 3.Vapor pressure 4. Surface tension 5. Mesoscopic theory of thermal conductivity 6. Mesoscopic theory of viscosity for liquids and solids 7. Brownian diffusion 8.…
We develop a theory based on relative entropy to show the uniqueness and L^2 stability (up to a translation) of extremal entropic Rankine-Hugoniot discontinuities for systems of conservation laws (typically 1-shocks, n-shocks, 1-contact…
We study the effects of strict conservation laws and the problem of negative contributions to final momentum distribution during the freeze out through 3-dimensional hypersurfaces with space-like normal. We study some suggested solutions…
In this paper we study the problem of the global existence (in time) of weak, entropic solutions to a system of three hyperbolic conservation laws, in one space dimension, for large initial data. The system models the dynamics of phase…
Hyperbolic systems under nonconservative form arise in numerous applications modeling physical processes, for example from the relaxation of more general equations (e.g. with dissipative terms). This paper reviews an existing class of…
For every mapping of a perturbed spacetime onto a background and with any vector field $\xi$ we construct a conserved covariant vector density $I(\xi)$, which is the divergence of a covariant antisymmetric tensor density, a…
When a plane shock hits a wedge head on, it experiences a reflection-diffraction process, and then a self-similar reflected shock moves outward as the original shock moves forward in time. The complexity of reflection-diffraction…
This paper describes a multidimensional hydrodynamic code which can be used for studies of relativistic astrophysical flows. The code solves the special relativistic hydrodynamic equations as a hyperbolic system of conservation laws based…
We address the Riemann and Cauchy problems for systems of $n$ conservation laws in $m$ unknowns which are subject to $m-n$ constraints ($m\geq n$). Such constrained systems generalize systems of conservation laws in standard form to include…
Inflow BC plays a critical role in the study of hyperbolic PDE in a bounded domain. We establish $W^{1,\infty}$ stability for 1D hyperbolic conservation laws with inflow data in a bounded interval, and $W^{2,3+}$ stability of a large class…
A pair of symmetric expressions for the second law of thermodynamics is put forward. The conservation and transfer of entropy is discussed and applied to problems like biology, culture and life itself. A new explanation is given to the…
As Physics did in previous centuries, there is currently a common dream of extracting generic laws of nature in economics, sociology, neuroscience, by focalising the description of phenomena to a minimal set of variables and parameters,…