Related papers: Group Analysis of Variable Coefficient Diffusion--…
Gauge invariant conservation laws for the linear and angular momenta are studied in a certain 2+1 dimensional first order dynamical model of vortices in superconductivity. In analogy with fluid vortices it is possible to express the linear…
The advection-diffusion equation can be approximated by a one-dimensional diffusion equation in Lagrangian coordinates along the directions of compression of fluid elements (the stable manifold). This result holds in any number of…
Motivated by many applications (geophysical flows, general relativity), we attempt to set the foundations for a study of entropy solutions to nonlinear hyperbolic conservation laws posed on a (Riemannian or Lorentzian) manifold. The flux of…
Conservation laws of a class of time-dependent damped nonlinear multidimensional wave equations are derived by Noether's theorem. For arbitrary nonzero damping coefficient and nonlinear interaction term, its infinitesimal variational…
We consider two physically and mathematically distinct regularization mechanisms of scalar hyperbolic conservation laws. When the flux is convex, the combination of diffusion and dispersion are known to give rise to monotonic and…
Dispersion curves to a oscillatory reaction-diffusion system with the self-consistent flow have obtained by means of numerical calculations. The flow modulates the shape of dispersion curves and characteristics of traveling waves. The point…
Given a first-order nonlinear hyperbolic system of conservation laws endowed with a convex entropy-entropy flux pair, we can consider the class of weak solutions containing shock waves depending upon some small scale parameters. In this…
Symmetry- and conservation law-preserving finite difference discretizations are obtained for linear and nonlinear one-dimensional wave equations on five- and nine-point stencils, using the theory of Lie point symmetries of difference…
We derive the Noether identities and the conservation laws for general gravitational models with arbitrarily interacting matter and gravitational fields. These conservation laws are used for the construction of the covariant equations of…
Using advantages of nonstandard computational techniques based on the light-cone variables, we explicitly find the algebra of generalized symmetries of the (1+1)-dimensional Klein-Gordon equation. This allows us to describe this algebra in…
Differential equations arising in fluid mechanics are usually derived from the intrinsic properties of mechanical systems, in the form of conservation laws, and bear symmetries, which are not generally preserved by a finite difference…
Extracting governing physical laws from computational or experimental data is crucial across various fields such as fluid dynamics and plasma physics. Many of those physical laws are dissipative due to fluid viscosity or plasma collisions.…
This paper improves a previously established test involving only coefficients to decide a priori whether or not non-trivial symmetries of a large class of space-time dependent diffusion processes on the real line exist. When the existence…
A heat equation with non-constant diffusivity depending as a power law on the spatial variable is analysed using Lie's method to identify classical point symmetries. It is shown that the group invariant solutions of a four-dimensional…
We formulate gauge invariance for the equilibrium statistical mechanics of classical multi-component systems. Species-resolved phase space shifting constitutes a gauge transformation which we analyze using Noether's theorem and shifting…
We analyze the conservation properties of various discretizations of the system of compressible Euler equations for shock-free flows, with special focus on the treatment of the energy equation and on the induced discrete equations for other…
We consider the highly nonlinear and ill-posed inverse problem of determining some general expression $F(x,t,u,\nabla_xu)$ appearing in the diffusion equation $\partial_tu-\Delta_x u+F(x,t,u,\nabla_xu)=0$ on $\Omega\times(0,T)$, with $T>0$…
We study the contribution of advection by thermal velocity fluctuations to the effective diffusion coefficient in a mixture of two identical fluids. The steady-state diffusive flux in a finite system subject to a concentration gradient is…
The field equations in the nonsymmetric gravitational theory are derived from a Lagrangian density using a first-order formalism. Using the general covariance of the Lagrangian density, conservation laws and tensor identities are derived.…
We show for a variety of classes of conservative PDEs that discrete gradient methods designed to have a conserved quantity (here called energy) also have a time-discrete conservation law. The discrete conservation law has the same conserved…