相关论文: Hydrodynamic equation for a deposition model

In this paper we introduce a new property of two-dimensional integrable systems -- existence of infinitely many local three-dimensional conservation laws for pairs of integrable two-dimensional commuting flows. Infinitely many…

Landau's excitation-based argument for superfluids -- that at temperature $T=0$ the normal fluid density $\rho_{n}$ is zero -- should also apply to supersolids. Further, for a total mass density $\rho$, Leggett argues that the superfluid…

We provide a detailed analysis of the boundary layers for mixed hyperbolic-parabolic systems in one space dimension and small amplitude regimes. As an application of our results, we describe the solution of the so-called boundary Riemann…

We study point and higher symmetries for the hydrodynamic-type systems with two independent variables $t$ and $x$ with and without explicit dependence of the equations on $t,x$. We consider those systems which possess an…

In this article, we discuss about the resolution of the Riemann problem for a 2x2 system in nonconservative form exhibiting parabolic degeneracy. The system can be perceived as the limiting equation (depending on a parameter tending to 0)…

We prove the decay of the L 2-distance from the solution u(t) of a hyperbolic scalar conservation law, to some convex, flow-invariant target sets.

A new two-component system with cubic nonlinearity and linear dispersion: \begin{eqnarray*} \left\{\begin{array}{l} m_t=bu_{x}+\frac{1}{2}[m(uv-u_xv_x)]_x-\frac{1}{2}m(uv_x-u_xv), \\ n_t=bv_{x}+\frac{1}{2}[ n(uv-u_xv_x)]_x+\frac{1}{2}…

This paper describes a class of scheme named "residual distribution schemes" or "fluctuation splitting schemes". They are a generalization of Roe's numerical flux in fluctuation form. The so-called multidimensional fluctuation schemes have…

The equivariant Hopf bifurcation dynamics of a class of system of partial differential equations is carefully studied. The connections between the current dynamics and fundamental concepts in hyperbolic conservation laws are explained. The…

In this paper, we consider mathematical modeling and numerical simulation of non-isothermal compressible multi-component diffuse-interface two-phase flows with realistic equations of state. A general model with general reference velocity is…

Recently, a hydrodynamic description of local equilibrium dynamics in quantum integrable systems was discovered. In the diffusionless limit, this is equivalent to a certain "Bethe-Boltzmann" kinetic equation, which has the form of an…

In this paper, we show that a geometrical condition on $2\times2$ systems of conservation laws leads to non-uniqueness in the class of 1D continuous functions. This demonstrates that the Liu Entropy Condition alone is insufficient to…

In this paper, two approaches for modeling three-component fluid flows using diffusive interface method are discussed. Thermodynamic consistency of the proposed models is preserved when using an energetic variational framework to derive the…

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…

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…

Motivated by many applications (geophysical flows, general relativity), we attempt to set the foundations for a study of entropy solutions to nonlinear hyperbolic conservation laws posed on a (Riemannian or Lorentzian) manifold. The flux of…

Via hydrodynamics preserving molecular dynamics simulations we study growth phenomena in a phase separating symmetric binary mixture model. We quench high-temperature homogeneous configurations to state points inside the miscibility gap,…

We consider a discrete dynamical system on a pseudo-Riemannian manifold and we determine the concept of a hyperbolic set for it. We insert a condition in the definition of a hyperbolic set which implies to the unique decomposition of a part…

We prove a hydrodynamic limit for ballistic deposition on a multidimensional lattice. In this growth model particles rain down at random and stick to the growing cluster at the first point of contact. The theorem is that if the initial…

We model two systems of two conservation laws defined on complementary spatial intervals and coupled by a moving interface as a single non-autonomous port-Hamiltonian system, and provide sufficient conditions for its Kato-stability. An…