相关论文: On the construction of conservation laws: a mixed …
In this work we study a generalized variable-coefficient Gardner equation from the point of view of Lie symmetries in partial differential equations. We find conservation laws by using the multipliers method of Anco and Bluman which does…
An effective algorithmic method is presented for finding the local conservation laws for partial differential equations with any number of independent and dependent variables. The method does not require the use or existence of a…
This paper gives a general treatment and proof of the direct conservation law method presented in Part I. In particular, the treatment here applies to finding the local conservation laws of any system of one or more partial differential…
The direct method of construction of local conservation laws of partial differential equations (PDE) is a systematic method applicable to a wide class of PDE systems [Anco S. and Bluman G., Direct construction method for conservation laws…
In this paper, we highlight the complimentary nature of the results of Anco & Bluman and Ibragimov in the construction of conservation laws; that whilst the former establishes the role of multipliers, the latter presents a formal procedure…
A conservation law theorem stated by N. Ibragimov along with its subsequent extensions are shown to be a special case of a standard formula that uses a pair consisting of a symmetry and an adjoint-symmetry to produce a conservation law…
We construct Lie point symmetries, a closed-form solution and conservation laws using a non-Noetherian approach for a specific case of the Gorini-Kossakowski-Sudarshan-Lindblad equation that has been recast for the study of non-relativistic…
Symmetry properties of conservation laws of partial differential equations are developed by using the general method of conservation law multipliers. As main results, simple conditions are given for characterizing when a conservation law…
We address the study of a class of 1D nonlocal conservation laws from a numerical point of view. First, we present an algorithm to numerically integrate them and prove its convergence. Then, we use this algorithm to investigate various…
This paper presents recent work on connections between symmetries and conservation laws. After reviewing Noether's theorem and its limitations, we present the Direct Construction Method to show how to find directly the conservation laws for…
We show that the so-called hidden potential symmetries considered in a recent paper [Gandarias M., Physica A, 2008, V.387, 2234-2242] are ordinary potential symmetries that can be obtained using the method introduced by Bluman and…
In this paper we consider convergence of approximate solutions of conservation laws. We start with an overview over the historical developments since the 1950s, and the analytical tools used in this context. Then we present some of our own…
The first part of this paper introduces sufficient conditions to determine conservation laws of diffusion equations of arbitrary fractional order in time. Numerical methods that satisfy a discrete analogue of these conditions have…
A novel structure-preserving numerical method to solve random hyperbolic systems of conservation laws is presented. The method uses a concept of generalized, measure-valued solutions to random conservation laws. This yields a linear partial…
Conservation and consistency are fundamental properties of discretizations of systems of hyperbolic conservation laws. Here, these concepts are extended to the realm of iterative methods by formally defining locally conservative and flux…
In this work we present a rather general approach to approximate the solutions of nonlocal conservation laws. In a first step, we approximate the nonlocal term with an appropriate quadrature rule applied to the spatial discretization. Then,…
The paper compares computational aspects of four approaches to compute conservation laws of single differential equations (DEs) or systems of them, ODEs and PDEs. The only restriction, required by two of the four corresponding computer…
Symmetries and conservation laws are studied for a generalized Westervelt equation which is a nonlinear partial differential equation modelling the propagation of sound waves in a compressible medium. This nonlinear wave equation is widely…
We prove that potential conservation laws have characteristics depending only on local variables if and only if they are induced by local conservation laws. Therefore, characteristics of pure potential conservation laws have to essentially…
This work extends the Ibragimov's conservation theorem for partial differential equations [{\it J. Math. Anal. Appl. 333 (2007 311-328}] to under determined systems of differential equations. The concepts of adjoint equation and formal…