相关论文: The Variational Bi-Complex for Systems of Semi-Lin…
For systems of partial differential equations in three spatial dimensions, dynamical conservation laws holding on volumes, surfaces, and curves, as well as topological conservation laws holding on surfaces and curves, are studied in a…
A method for symbolically computing conservation laws of nonlinear partial differential equations (PDEs) in multiple space dimensions is presented in the language of variational calculus and linear algebra. The steps of the method are…
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…
Based on Lie group method, potential symmetry and invariant solutions for generalized quasilinear hyperbolic equations are studied. To obtain the invariant solutions in explicit form, we focus on the physically interesting situations which…
In this paper we study the deformations of bihamiltonian PDEs of hydrodynamic type with one dependent variable. The reason we study such deformations is that the deformed systems maintain an infinite number of commuting integrals of motion…
This paper is the second in a series of works dedicated to studying non-linear partial differential equations via derived geometric methods. We study a natural derived enhancement of the de Rham complex of a non-linear PDE via…
We consider the application of finite element exterior calculus (FEEC) methods to a class of canonical Hamiltonian PDE systems involving differential forms. Solutions to these systems satisfy a local multisymplectic conservation law, which…
We present a framework for constructing a first-order hyperbolic system whose solution approximates that of a desired higher-order evolution equation. Constructions of this kind have received increasing interest in recent years, and are…
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…
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…
This paper presents a high-order discontinuous Galerkin finite element method to solve the barotropic version of the conservative symmetric hyperbolic and thermodynamically compatible (SHTC) model of compressible two-phase flow, introduced…
A method of integrable discretization of the Liouville type nonlinear partial differential equations is suggested based on integrals. New examples of discrete Liouville type models are presented.
In this article we are interested in the boundary stabilization in finite time of one-dimensional linear hyperbolic balance laws with coefficients depending on time and space. We extend the so called "backstepping method" by introducing…
Dynamical PDEs that have a spatial divergence form possess conservation laws that involve an arbitrary function of time. In one spatial dimension, such conservation laws are shown to describe the presence of an $x$-independent source/sink;…
Conservation laws are computed for various nonlinear partial differential equations that arise in elasticity and acoustics. Using a scaling homogeneity approach, conservation laws are established for two models describing shear wave…
Many PDEs (Burgers' equation, KdV, Camassa-Holm, Euler's fluid equations,...) can be formulated as infinite-dimensional Lie-Poisson systems. These are Hamiltonian systems on manifolds equipped with Poisson brackets. The Poisson structure is…
The paper concerns boundary value problems for general nonautonomous first order quasilinear hyperbolic systems in a strip. We construct small global classical solutions, assuming that the right hand sides are small. In the case that all…
Existing model reduction techniques for high-dimensional models of conservative partial differential equations (PDEs) encounter computational bottlenecks when dealing with systems featuring non-polynomial nonlinearities. This work presents…
We prove the well posedness of a class of non linear and non local mixed hyperbolic-parabolic systems in bounded domains, with Dirichlet boundary conditions. In view of control problems, stability estimates on the dependence of solutions on…
We approach the construction of Backlund transformations for Darboux integrable hyperbolic partial differential equations in the plane through the reduction of exterior differential systems. For example it is shown that all the Backlund…