Related papers: An analog of the variational derivative and constr…
Hyperbolic problems can at times be solved employing symbolic arguments. This is especially true for the construction of forward (and backward) fundamental solutions. We formulate a corresponding abstract scheme and illustrate its…
The aim of this paper is to investigate the fractional combinatorial Calabi flow for hyperbolic bordered surfaces. By Lyapunov theory, it is proved that the flow exists for all time and converges exponentially to a conformal factor that…
A stochastic Galerkin formulation for a stochastic system of balanced or conservation laws may fail to preserve hyperbolicity of the original system. In this work, we develop hyperbolicity-preserving stochastic Galerkin formulation for the…
We develop method that allows to derive reductions and solutions to hyperbolic systems of partial differential equations. The method is based on using functions that are constant in the direction of characteristics of the system. These…
We study the problem of constructing systems of hyperbolic conservation laws in one space dimension with prescribed eigencurves, i.e. the eigenvector fields of the Jacobian of the flux are given. We formulate this as a typically…
Dipole-conserving fluids serve as examples of kinematically constrained systems that can be understood on the basis of symmetry. They are known to display various exotic features including glassylike dynamics, subdiffusive transport, and…
Integrability conditions for difference equations admitting a second order formal recursion operator are presented and the derivation of symmetries and canonical conservation laws is discussed. In the generic case, nonlocal conservation…
The causal structure of Einstein's evolution equations is considered. We show that in general they can be written as a first order system of balance laws for any choice of slicing or shift. We also show how certain terms in the evolution…
We show that the two-component system of hyperbolic conservation laws $\partial_t \rho + \partial_x (\rho u) =0 = \partial_t u + \partial_x \rho$ appears naturally in the formally computed hydrodynamic limit of some randomly growing…
We prove the well--posedness of a dynamical perfect plasticity model under general assumptions on the stress constraint set and on the reference configuration. The problem is studied by combining both calculus of variations and hyperbolic…
This survey article describes the algorithmic approaches successfully used over the time to construct hyperbolic structures on 3-dimensional topological "objects" of various types, and to classify several classes of such objects using such…
We would like to formulate relativistic dissipative hydrodynamics for multi-component systems with multiple conserved currents. This is important for analyses of the hot matter created in relativistic heavy ion collisions because particle…
By a semi-Lagrangian change of coordinates, the hydrostatic Euler equations describing free-surface sheared flows is rewritten as a system of quasilinear equations, where stability conditions can be determined by the analysis of its…
In this paper we present an approach to approximate numerically the solution of coupled hyperbolic conservation laws. The coupling is achieved through a fixed interface, in which interface conditions are linking the traces of both sides.…
In supersymmetric quantum mechanics, shape invariance is a sufficient condition for solvability. We show that all conventional additive shape invariant superpotentials that are independent of $\hbar$ obey two partial differential equations.…
The scaling of the exact solution of a hyperbolic balance law generates a family of scaled problems in which the source term does not depend on the current solution. These problems are used to construct a sequence of solutions whose…
The one-dimensional modified shallow water equations in Lagrangian coordinates are considered. It is shown the relationship between symmetries and conservation laws in Lagrangian coordinates, in mass Lagrangian variables, and Eulerian…
We present some recent developments on shock capturing methods for nonlinear hyperbolic systems of balance laws, whose prototype is the Euler system of compressible fluid flows, and especially discuss {structure-preserving} techniques. The…
We present a conservative/dissipative time integration scheme for nonlinear mechanical systems. Starting from a weak form, we derive algorithmic forces and velocities that guarantee the desired conservation/dissipation properties. Our…
Aim of this paper is to review some basic ideas and recent developments in the theory of strictly hyperbolic systems of conservation laws in one space dimension. The main focus will be on the uniqueness and stability of entropy weak…