Conservation Laws of Multidimensional Diffusion–Convection Equations
نویسنده
چکیده
All possible linearly independent local conservation laws for n-dimensional diffusion–convection equations ut = (A(u))ii +(B i(u))i were constructed using the direct method and the composite variational principle. Application of the method of classification of conservation laws with respect to the group of point transformations [R.O. Popovych, N.M. Ivanova, J. Math. Phys., 2005, V.46, 043502 (math-ph/0407008)] allows us to formulate the result in explicit closed form. Action of the symmetry groups on the conservation laws of diffusion equations is investigated and generating sets of conservation laws are constructed.
منابع مشابه
Conservation Laws and Potential Systems of Diffusion-Convection Equations
In her famous paper [14] Emmy Noether proved that each Noether symmetry associated with a Lagrangian generates a conservation law. (Modern treatment of relationship between components of Noether conserved vector and Lie–Bäcklund operators which are Noether symmetries was adduced in [10,18]. Kara et al [12,13] constructed conservation laws of some classes of PDEs with two independent variables u...
متن کاملA Third-Order Semidiscrete Central Scheme for Conservation Laws and Convection-Diffusion Equations
We present a new third-order, semidiscrete, central method for approximating solutions to multidimensional systems of hyperbolic conservation laws, convection-diffusion equations, and related problems. Our method is a high-order extension of the recently proposed second-order, semidiscrete method in [A. Kurgonov and E. Tadmor, J. Comput Phys., 160 (2000) pp. 241–282]. The method is derived inde...
متن کاملHierarchy of Conservation Laws of Diffusion–Convection Equations
We introduce notions of equivalence of conservation laws with respect to Lie symmetry groups for fixed systems of differential equations and with respect to equivalence groups or sets of admissible transformations for classes of such systems. We also revise the notion of linear dependence of conservation laws and define the notion of local dependence of potentials. To construct conservation law...
متن کاملA Basis of Conservation Laws for Partial Differential Equations
The classical generation theorem of conservation laws from known ones for a system of differential equations which uses the action of a canonical Lie–Bäcklund generator is extended to include any Lie–Bäcklund generator. Also, it is shown that the Lie algebra of Lie–Bäcklund symmetries of a conserved vector of a system is a subalgebra of the Lie–Bäcklund symmetries of the system. Moreover, we in...
متن کاملConservation Laws of Variable Coefficient Diffusion–Convection Equations
We study local conservation laws of variable coefficient diffusion–convection equations of the form f(x)ut = (g(x)A(u)ux)x + h(x)B(u)ux. The main tool of our investigation is the notion of equivalence of conservation laws with respect to the equivalence groups. That is why, for the class under consideration we first construct the usual equivalence group G∼ and the extended one Ĝ∼ including tran...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008