Related papers: Conservation law for a fourth order elliptic syste…
Lions, Perthame, Tadmor conjectured in 1994 an optimal smoothing effect for entropy solutions of nonlinear scalar conservations laws . In this short paper we will restrict our attention to the simpler one-dimensional case. First,…
Using a manifestly invariant Lagrangian density based on Clebsch fields and suitable for geophysical fluid dynamics, the conservation of mass, entropy, momentum and energy, and the associated symmetries are investigated. In contrast, it is…
In this paper, a critical fourth-order Kirchhoff type elliptic equation with a subcritical perturbation is studied. The main feature of this problem is that it involves both a nonlocal coefficient and a critical term, which bring essential…
In the context of departures from Special Relativity written as a momentum power expansion in the inverse of an ultraviolet energy scale M, we derive the constraints that the relativity principle imposes between coefficients of a deformed…
The one-dimensional viscous conservation law is considered on the whole line $$ u_t + f(u)_x=\eps u_{xx},\quad (x,t)\in\RR\times\overline{\RP},\quad \eps>0, $$ subject to positive measure initial data. The flux $f\in C^1(\RR)$ is assumed to…
The explicit formulation of the general inverse problem on conservation laws is presented for the first time. In this problem one aims to derive the general form of systems of differential equations that admit a prescribed set of…
It is widely accepted that conservation laws, especially energy-momentum conservation, have fundamental importance for both classical and quantum systems in physics. A widely used method to derive the conservation laws is based on Noether's…
We provide an elementary proof of geometric synchronisation for scalar conservation laws on a domain with Dirichlet boundary conditions. Unlike previous results, our proof does not rely on a strict maximum principle, and builds instead on a…
In this paper we consider finite dimensional dynamical systems generated by a Lipschitz function. We prove a version of the Whitney's Extension Theorem on compact manifolds to obtain a version of the well-known Lambda Lemma for Lipschitz…
Superintegrable Hamiltonian systems in a two-dimensional Euclidean space are considered. We present all real standard potentials that allow separation of variables in polar coordinates and admit an independent fourth-order integral of…
The self-adjoint sub-classes of nonlinear evolution equations of fourth-order with time dependent coefficients are determined, generalizing some recent results. Using the new conservation theorem recently proved by Nail Ibragimov some…
For nonlinear Schroedinger equations with a power nonlinearity, a new approach to derive the conservation law of the momentum and the pseudo conformal conservation law is obtained. Since this approach does not contain approximating…
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…
We give an infinitary extension of the Ne\v{s}et\v{r}il-R\"{o}dl theorem for category of relational structures with special type-respecting embeddings.
We consider arbitrary discrete probability laws on the real line. We obtain a criterion of their belonging to a new class of quasi-infinitely divisible laws, which is a wide natural extension of the class of well known infinitely divisible…
The zero curvature representation of Zakharov and Shabat has been generalized recently to higher dimensions and has been used to construct non-linear field theories which either are integrable or contain integrable submodels. The Skyrme…
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…
We derive conservation laws for energy-momentum (canonical and dynamical) and angular momentum for a general Lorentz connection.
Non-local systems of conservation laws play a crucial role in modeling flow mechanisms across various scenarios. The well-posedness of such problems is typically established by demonstrating the convergence of robust first-order schemes.…
High-order reconstruction schemes for the solution of hyperbolic conservation laws in orthogonal curvilinear coordinates are revised in the finite volume approach. The formulation employs a piecewise polynomial approximation to the…