Related papers: Extension the Noether's theorem to Lagrangian form…
We establish local-in-time existence and uniqueness results for nonlocal conservation laws with a nonlinear mobility, in several space dimensions, under weak assumptions on the kernel, which is assumed to be bounded and of finite total…
Conservation laws have many applications in numerical relativity. However, it is not straightforward to define local conservation laws for general dynamic spacetimes due the lack of coordinate translation symmetries. In flat space, the rate…
Validity of local equilibrium has been questioned for non-equilibrium systems which are characterized by delayed response. In particular, for systems with non-zero thermodynamic inertia, the assumption of local equilibrium leads to negative…
We prove a Noether type symmetry theorem to fractional problems of the calculus of variations with classical and Riemann-Liouville derivatives. As result, we obtain constants of motion (in the classical sense) that are valid along the mixed…
Nonlocal gravity (NLG) is a classical nonlocal generalization of Einstein's theory of gravitation based on a certain analogy with the nonlocal electrodynamics of media. The history dependence enters NLG through a constitutive relation…
Flows of one-dimensional continuum in Lagrangian coordinates are studied in the paper. Equations describing these flows are reduced to a single Euler-Lagrange equation which contains two undefined functions. Particular choices of the…
The concept of nonlinear self-adjointness is employed to construct the conservation laws for fractional evolution equations using its Lie point symmetries. The approach is demonstrated on subdiffusion and diffusion-wave equations with the…
We prove that on the condition of non-trivial solutions, the Euler-Lagrange and Noether equations are equivalent for the variational problem of nonlinear Poisson equation and a class of more general Lagrangians, including position…
In this second part of the paper, we consider finite difference Lagrangians which are invariant under linear and projective actions of $SL(2)$, and the linear equi-affine action which preserves area in the plane. We first find the…
We review the Lagrangian formulation of Noether symmetries (as well as "generalized Noether symmetries") in the framework of Calculus of Variations in Jet Bundles, with a special attention to so-called "Natural Theories" and "Gauge-Natural…
In some models involving nonlinear conservation laws, physical mechanisms exist which prevent the formation of shocks. This gives rise to conservation laws with a constraint on the gradient of the solution. We approach this problem by…
Noether's theorem and the invariances of the Willmore functional are used to derive conservation laws that are satisfied by the critical points of the Willmore energy subject to generic constraints. We recover in particular previous results…
This paper presents a formulation of Noether's theorem for fractional classical fields. We extend the variational formulations for fractional discrete systems to fractional field systems. By applying the variational principle to a…
In the light of the local Lorentz transformations and the general Noether theorem, a new formulate of the general covariant angular momentum conservation law in Einstein-Cartan gravitation theory is obtained, which overcomes the critical…
We show how Noether conservation laws can be obtained from the particle relabelling symmetries in the Euler-Poincar\'e theory of ideal fluids with advected quantities. All calculations can be performed without Lagrangian variables, by using…
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.…
A variational principle for Lagrangian densities containing derivatives of real order is formulated and the invariance of this principle is studied in two characteristic cases. Necessary and sufficient conditions for an infinitesimal…
A generalization of the KP equation involving higher-order dispersion is studied. This equation appears in several physical applications. As new results, the Lie point symmetries are obtained and used to derive conservation laws via…
A hybrid framework is developed that highlights and unifies the most important aspects of the Noether correspondence between symmetries and conserved integrals in Lagrangian and Hamiltonian mechanics. Several main results are shown: (1) a…
Making use of the Lagrange anchor construction introduced earlier to quantize non-Lagrangian field theories, we extend the Noether theorem beyond the class of variational dynamics.