相关论文: Symmetries of Conservation Laws
The paper aims to study the connection between symmetries and conservation laws for the 2D Ricci flow model. The procedure starts by obtaining a set of multipliers which generates conservation laws. Then, using a general relation which…
We describe $\delta$ shock wave arising from continuous initial data in the case of triangular conservation law system arising from "generalized pressureless gas dynamics model". We use the weak asymptotic method.
In this paper, we propose an adaptive high-order method for hyperbolic systems of conservation laws. The proposed method is based on a dual formulation approach: Two numerical solutions, corresponding to conservative and nonconservative…
A simple characterization of the action of symmetries on conservation laws of partial differential equations is studied by using the general method of conservation law multipliers. This action is used to define symmetry-invariant and…
The idea of using fast sweeping methods for solving stationary systems of conservation laws has previously been proposed for efficiently computing solutions with sharp shocks. We further develop these methods to allow for a more challenging…
For static reductions of isotropic and anisotropic Magnetohydrodynamics plasma equilibrium models, a complete classification of admitted point symmetries and conservation laws up to first order is presented. It is shown that the symmetry…
A simple conservation law formula for field equations with a scaling symmetry is presented. The formula uses adjoint-symmetries of the given field equation and directly generates all local conservation laws for any conserved quantities…
The Szekeres system is studied with two methods for the determination of conservation laws. Specifically we apply the theory of group invariant transformations and the method of singularity analysis. We show that the Szekeres system admits…
Existence and admissibility of $\delta$-shock type solution is discussed for the following nonconvex strictly hyperbolic system arising in studues of plasmas: \pa_t u + \pa_x \big(\Sfrac{u^2+v^2}{2} \big) &=0 \pa_t v +\pa_x(v(u-1))&=0. The…
A fifth-order KdV equation with time dependent coefficients and linear damping has been studied. Symmetry groups have several different applications in the context of nonlinear differential equations. For instance, they can be used to…
In this work, we introduce a novel approach to formulating an artificial viscosity for shock capturing in nonlinear hyperbolic systems by utilizing the property that the solutions of hyperbolic conservation laws are not reversible in time…
We show uniqueness and stability in $L^2$ and for all time for piecewise-smooth solutions to hyperbolic balance laws. We have in mind applications to gas dynamics, the isentropic Euler system and the full Euler system for a polytropic gas…
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…
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…
We consider a strictly hyperbolic, genuinely nonlinear system of conservation laws in one space dimension. A sharp decay estimate is proved for the positive waves in an entropy weak solution. The result is stated in terms of a partial…
In this paper, we study stability properties of solutions to scalar conservation laws with a class of non-convex fluxes. Using the theory of $a$-contraction with shifts, we show $L^2$-stability for shocks among a class of large…
We consider solutions of hyperbolic conservation laws regularized with vanishing diffusion and dispersion terms. Following a pioneering work by Schonbek, we establish the convergence of the regularized solutions toward discontinuous…
Fast sweeping methods have become a useful tool for computing the solutions of static Hamilton-Jacobi equations. By adapting the main idea behind these methods, we describe a new approach for computing steady state solutions to systems of…
We propose a parametric hyperbolic conservation law (SymCLaw) for learning hyperbolic systems directly from data while ensuring conservation, entropy stability, and hyperbolicity by design. Unlike existing approaches that typically enforce…
We find a representation of smooth solutions to the Cauchy problem for a scalar multidimensional conservation law as small diffusion limit of a stochastic perturbation along characteristics. It helps, in particular, to study the process of…