相关论文: Hierarchy of Conservation Laws of Diffusion--Conve…

Using a four-dimensional manifestly covariant formalism suitable for classical fluid dynamics, it is shown that the conservation of potential vorticity is not associated with any symmetry of the equations of motion but is instead a trivial…

In the paper the role of conservation laws in evolutionary processes, which proceed in material systems (in material media) and lead to generation of physical fields, is shown using skew-symmetric differential forms. In present paper the…

Nonlinear self-adjointness method for constructing conservation laws of partial differential equations (PDEs) is further studied. We show that any adjoint symmetry of PDEs is a differential substitution of nonlinear self-adjointness and…

English version of abstract: The dynamic optimization problems treated by the calculus of variations are usually solved with the help of the 2nd order Euler-Lagrange differential equations. These equations are, generally speaking,…

Scalar conservation laws in one space variable allow a Lagrangian (particle path) formulation. The Lagrangian trajectory in the infinite-dimensional group of diffeomorphisms on the physical space can be written as a system of conservation…

We analyze Non-linear chaffee infatne equation by groups theoretical method to get its symmetries and conservation laws.

The usual heat equation is not suitable to preserve the topology of divergence-free vector fields, because it destroys their integral line structure. On the contrary, in the fluid mechanics literature, on can find examples of…

We prove that any potential symmetry of a system of evolution equations reduces to a Lie symmetry through a nonlocal transformation of variables. Based on this fact is our method of group classification of potential symmetries of systems of…

This paper investigates a system of nonlinear reaction-diffusion equations modeling the industrial synthesis of ammonia. By applying Lie group analysis, we construct self-similar solutions and derive a reduced system of ordinary…

In this paper, we propose a modified formal Lagrangian formulation by introducing dummy dependent variables and prove the existence of such a formulation for any system of differential equations. The corresponding Euler--Lagrange equations,…

We introduce novel approximate systems for dispersive and diffusive-dispersive equations with nonlinear fluxes. For purely dispersive equations, we construct a first-order, strictly hyperbolic approximation. Local well-posedness of smooth…

We develop a method of obtaining a hierarchy of new higher-order entropies in the context of compressible models with local and non-local diffusion and isentropic pressure. The local viscosity is allowed to degenerate as the density…

The dynamics of dislocations can be formulated in terms of the evolution of continuous variables representing dislocation densities ('continuum dislocation dynamics'). We show for various variants of this approach that the resulting models…

Solutions to hyperbolic conservation laws can be approximated in many different ways: by vanishing viscosity, relaxations, discrete or semi-discrete numerical schemes, approximation with a nonlocal flux, etc$\ldots$ For some of these…

Potential equivalence transformations (PETs) are effectively applied to a class of nonlinear diffusion-convection equations. For this class all possible potential symmetries are classified and a theorem on connection of them with point ones…

In this work we propose a new, arbitrary order space-time finite element discretisation for Hamiltonian PDEs in multisymplectic formulation. We show that the new method which is obtained by using both continuous and discontinuous…

We study a class of degenerate convection diffusion equations with a fractional nonlinear diffusion term. These equations are natural generalizations of anomalous diffusion equations, fractional conservations laws, local convection…

A new, general, field theoretic approach to the derivation of asymptotic conservation laws is presented. In this approach asymptotic conservation laws are constructed directly from the field equations according to a universal prescription…

Parameterization (closure) schemes in numerical weather and climate prediction models account for the effects of physical processes that cannot be resolved explicitly by these models. Methods for finding physical parameterization schemes…

We determine the Lie point symmetries of a class of BBM-KdV systems and establish its nonlinear self-adjointness. We then construct conservation laws via Ibragimov's Theorem.