Related papers: Group Analysis of Variable Coefficient Diffusion--…
We study invariant solutions of a certain class of time-fractional diffusion-wave equations with variable coefficients via Lie symmetry analysis. In physics, the fractional diffusion equation describes transport dynamics that are governed…
We establish the equations which translate a conservation law for the problem of the seismic response of an above-ground structure (e.g., building, hill or mountain) of arbitrary shape and inquire whether both the implicit (formal) and…
In the works by the author it has been shown that the conservation laws for material media (the conservation laws for energy, linear momentum, angular momentum, and mass, that establish a balance between the variation of a physical quantity…
We provide a complete classification of point symmetries and low-order local conservation laws of the generalized quasilinear KdV equation in terms of the arbitrary function. The corresponding interpretation of symmetry transformation…
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…
The method of preliminary group classification is rigorously defined, enhanced and related to the theory of group classification of differential equations. Typical weaknesses in papers on this method are discussed and strategies to overcome…
In Physica A vol 387(24) (2008) pp6079-6094 [1], a kinetic equation for gas flows was proposed that leads to a set of four macroscopic conservation equations, rather than the traditional set of three equations. The additional equation…
The present paper is focused on the analysis of the one-dimensional relativistic gas dynamics equations. The studied equations are considered in Lagrangian description, making it possible to find a Lagrangian such that the relativistic gas…
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,…
The appearance of a geometric flow in the conservation law of particle number in classical particle diffusion and in the conservation law of probability in quantum mechanics is discussed in the geometrical environment of a two-dimensional…
The paper is concerned with a scalar conservation law with discontinuous gradient-dependent flux. Namely, the flux is described by two different functions $f(u)$ or $g(u)$, when the gradient $u_x$ of the solution is positive or negative,…
For the Euler equations governing compressible isentropic fluid flow with a barotropic equation of state (where pressure is a function only of the density), local conservation laws in $n>1$ spatial dimensions are fully classified in two…
A large class of first order partial nonlinear differential equations in two independent variables which possess an infinite set of polynomial conservation laws derived from an explicit generating function is constructed. The conserved…
The paper deals with perturbations of the equation that have a number of conservation laws. When a small term is added to the equation its conserved quantities usually decay at individual rates, a phenomenon known as a selective decay.…
General self-consistent expressions for the coefficients of diffusion and dynamical friction in a stable, bound, multicomponent self-gravitating and inhomogeneous system are derived. They account for the detailed dynamics of the colliding…
The formulation of combinatorial differential forms, proposed by Forman for analysis of topological properties of discrete complexes, is extended by defining the operators required for analysis of physical processes dependent on scalar…
In this paper we form a general conservation law that unifies a class of physics field theories. For this we first introduce the notion of a general field as a formal sum differential forms on a Minkowski manifold. Thereafter, we employ the…
We find the Lie point symmetries of the Novikov equation and demonstrate that it is strictly self-adjoint. Using the self-adjointness and the recent technique for constructing conserved vectors associated with symmetries of differential…
We investigate $n$-component systems of conservation laws that possess third-order Hamiltonian structures of differential-geometric type. The classification of such systems is reduced to the projective classification of linear congruences…
Making sense of complex inhomogeneous systems composed of many interacting species is a grand challenge that pervades basically all natural sciences. Phase separation and pattern formation in reaction-diffusion systems have been largely…