相关论文: Conservation Laws of Variable Coefficient Diffusio…

In the work it has been shown that there are two types of the conservation laws. 1. The conservation laws that can be called exact ones. They point to an avalability of some conservative quantities or objects. Such objects are the physical…

We investigate the possible form of local translation invariant conservation laws associated with the relativistic field equations $\partial\bar\partial\phi_i=-v_i(\bphi)$ for a multicomponent field $\bphi$. Under the assumptions that…

Conservation laws are discussed in conjunction with quantum-mechanical indeterminacies of the corresponding observables. The considered examples show that the connections between energy and its indeterminacy may be quite intricate. The…

For systems of partial differential equations in three spatial dimensions, dynamical conservation laws holding on volumes, surfaces, and curves, as well as topological conservation laws holding on surfaces and curves, are studied in a…

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

Generalizing results of \cite{MC,S} and \cite{HSZ} for certain model reaction-diffusion and reaction-convection-diffusion equations, we derive and rigorously justify weakly nonlinear amplitude equations governing general Turing bifurcation…

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.…

We approximate a diffusion equation with highly oscillatory coefficients with a diffusion equation with constant coefficients. The approach is put in action in contexts where only partial information (namely the global energy stored in the…

The spatial discretization of convective terms in compressible flow equations is studied from an abstract viewpoint, for finite-difference methods and finite-volume type formulations with cell-centered numerical fluxes. General conditions…

I consider the geometry of the general class of scalar 2nd-order differential equations with parabolic symbol, including non-linear and non-evolutionary parabolic equations. After defining the appropriate $G$-structure to model parabolic…

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,…

We investigate the long time behaviour of the $L^2$-energy of solutions to wave equations with variable speed. The novelty of the approach is the combination of estimates for higher order derivatives of the coefficient with a stabilisation…

It is shown that the Kadanoff-Baym equations at consistent first-order gradient approximation reveal exact rather than approximate conservation laws related to global symmetries of the system. The conserved currents and energy-momentum…

We establish a version of the first Noether Theorem, according to which the (equivalence classes of) conserved quantities of given Euler-Lagrange equations in several independent variables are in one-to-one correspondence with the…

Lie symmetry group method is applied to study for the higher order Camassa-Holm equation. The symmetry group and its optimal system are given. Furthermore, preliminary classification of its group invariant solutions, symmetry reduction and…

We are concerned with fully-discrete schemes for the numerical approximation of diffusive-dispersive hyperbolic conservation laws with a discontinuous flux function in one-space dimension. More precisely, we show the convergence of…

We consider difference equations of order four and determine the one parameter Lie group of transformations (Lie symmetries) that leave them invariant. We introduce a technique for finding their first integrals and discuss the association…

In this paper, we proved that by choosing the proper variational function and variables, the variational approach proposed by M. Doi in soft matter physics was equivalent to the Conservation-Dissipation Formalism. To illustrate the…

The exhaustive group classification of the class of KdV-like equations with time-dependent coefficients $u_t+uu_x+g(t)u_{xxx}+h(t)u=0$ is carried out using equivalence based approach. A simple way for the construction of exact solutions of…

We apply the shifted composition rule -- an information-theoretic principle introduced in our earlier work [AC23] -- to establish shift Harnack inequalities for the Langevin diffusion. We obtain sharp constants for these inequalities for…