Related papers: A geometric approach to error estimates for conser…
The explicit formulation of the general inverse problem on conservation laws is presented for the first time. In this problem one aims to derive the general form of systems of differential equations that admit a prescribed set of…
We present the derivation of the hydrodynamic limit under Eulerian scaling for a general class of one-dimensional interacting particle systems with two or more conservation laws. Following Yau's relative entropy method it turns out that in…
We numerically solve fully (3+1)-dimensional relativistic hydrodynamical equation with the baryon number conservation law. For realistic initial conditions we adopt the results from the event generator (URASiMA). Using this model we discuss…
We prove the following dichotomy for vector fields in a C1-residual subset of volume-preserving flows: for Lebesgue almost every point all Lyapunov exponents equal to zero or its orbit has a dominated splitting. As a consequence if we have…
This work is concerned with ($N$-component) hyperbolic system of balance laws in arbitrary space dimensions. Under entropy dissipative assumption and the Shizuta-Kawashima algebraic condition, a general theory on the well-posedness of…
We consider general, non-linear curvature perturbations on scales greater than the Hubble horizon scale by invoking an expansion in spatial gradients, the so-called gradient expansion. After reviewing the basic properties of the gradient…
The flow of the relativistic imperfect fluid in two dimensions is discussed. We calculate the symmetry group of the energy-momentum tensor conservation equation in the ultrarelativistic limit. Group-invariant solutions for the…
The paper considers the plane one-dimensional flows for magnetohydrodynamics in the mass Lagrangian coordinates. The inviscid, thermally non-conducting medium is modeled by a polytropic gas. The equations are examined for symmetries and…
Hamiltonian and Lagrangian formulations for the two-dimensional quasi-geostrophic equations linearized about a zonally-symmetric basic flow are presented. The Lagrangian and Hamiltonian exhibit an infinite U(1) symmetry due to the absence…
Incompressible two-dimensional flows such as the advection (Liouville) equation and the Euler equations have a large family of conservation laws related to conservation of area. We present two Eulerian numerical methods which preserve a…
We derive a representation formula for the tensorial wave equation $\Box_\bg \phi^I=F^I$ in globally hyperbolic Lorentzian spacetimes $(\M^{2+1}, \bg)$ by giving a geometric formulation of the method of descent which is applicable for any…
We study pathwise entropy solutions for scalar conservation laws with inhomogeneous fluxes and quasilinear multiplicative rough path dependence. This extends the previous work of Lions, Perthame and Souganidis who considered spatially…
In the present contribution, we investigate first-order nonlinear systems of partial differential equations which are constituted of two parts: a system of conservation laws and non-conservative first order terms. Whereas the theory of…
The use of limiting methods for high-order numerical approximations of hyperbolic conservation laws generally requires defining an admissible region/bounds for the solution. In this work, we present a novel approach for computing solution…
We consider a hyperbolic system of three conservation laws in one space variable. The system is a model for fluid flow allowing phase transitions; in this case the state variables are the specific volume, the velocity and the mass density…
In this paper, we mainly study the integrability of 1+1 dimensional dispersive long-wave equation. Firstly, the Lie symmetry analysis of the equation is carried out in the first part. And the optimal system of the equation is obtained…
We investigate the well-posedness of scalar conservation laws whose flux depends on the solution both pointwise and nonlocally through integral averages. Our analysis is based on a fixed-point formulation, in which the nonlocal dependence…
We introduce a general framework for the construction of well-balanced finite volume methods for hyperbolic balance laws. We use the phrase well-balancing in a broader sense, since our proposed method can be applied to exactly follow any…
In this article we study intrusive uncertainty quantification schemes for systems of conservation laws with uncertainty. Standard intrusive methods lead to oscillatory solutions which sometimes even cause the loss of hyperbolicity. We…
We establish the equations which translate a conservation law for the problem of the seismic response of an above-ground structure (e.g., building, hill or mountain) of arbitrary shape and inquire whether both the implicit (formal) and…