Construction of potential systems for systems of PDEs with multi-dimensional spaces of conservation laws
نویسنده
چکیده
In this paper we consider generalization of procedure of construction of potential systems for systems of partial differential equations with multidimensional spaces of conservation laws. More precisely, for construction of potential systems in cases when dimension of the space of local conservation laws is greater than one, instead of using only basis conservation laws we use their arbitrary linear combinations being inequivalent with respect to equivalence group of the class of systems or symmetry group of the fixed system. It appears that the basis conservation laws can be equivalent with respect to groups of symmetry or equivalence transformations, or vice versa, the number of independent in this sense linear combinations of conservation laws can be grater than the dimension of the space of conservation laws. The first possibility leads to an unnecessary, often cumbersome, investigation of equivalent systems, the second one makes possible missing a great number of inequivalent potential systems. Examples of all these possibilities are given.
منابع مشابه
Self-similar solutions of the Riemann problem for two-dimensional systems of conservation laws
In this paper, a new approach is applied to study the self-similar solutions of 2×2 systems of nonlinear hyperbolic conservation laws. A notion of characteristic directions is introduced and then used to construct local and smooth solutions of the associated Riemann problem
متن کاملNew variants of the global Krylov type methods for linear systems with multiple right-hand sides arising in elliptic PDEs
In this paper, we present new variants of global bi-conjugate gradient (Gl-BiCG) and global bi-conjugate residual (Gl-BiCR) methods for solving nonsymmetric linear systems with multiple right-hand sides. These methods are based on global oblique projections of the initial residual onto a matrix Krylov subspace. It is shown that these new algorithms converge faster and more smoothly than the Gl-...
متن کاملAlgebraic Dichotomies with an Application to the Stability of Riemann Solutions of Conservation Laws
Recently, there has been some interest on the stability of waves where the functions involved grow or decay at an algebraic rate |x|m. In this paper we define the so called algebraic dichotomy that may aid in treating such problems. We discuss the basic properties of the algebraic dichotomy, methods of detecting it, and calculating the power of the weight function. We present several examples: ...
متن کاملMultidimensional partial differential equation systems: Nonlocal symmetries, nonlocal conservation laws, exact solutions
For systems of partial differential equations PDEs with n 3 independent variables, construction of nonlocally related PDE systems is substantially more complicated than is the situation for PDE systems with two independent variables. In particular, in the multidimensional situation, nonlocally related PDE systems can arise as nonlocally related subsystems as well as potential systems that follo...
متن کاملThe comparison of two high-order semi-discrete central schemes for solving hyperbolic conservation laws
This work presents two high-order, semi-discrete, central-upwind schemes for computing approximate solutions of 1D systems of conservation laws. We propose a central weighted essentially non-oscillatory (CWENO) reconstruction, also we apply a fourth-order reconstruction proposed by Peer et al., and afterwards, we combine these reconstructions with a semi-discrete central-upwind numerical flux ...
متن کامل