相关论文: Potential Conservation Laws

In this paper, we prove the uniqueness of energy conservative Holder continuous weak solution to a general quasilinear wave equation by the analysis of characteristics. This result has no restriction on the size of solutions, i.e. it is a…

The well posedness for a class of non local systems of conservation laws in a bounded domain is proved and various stability estimates are provided. This construction is motivated by the modelling of crowd dynamics, which also leads to…

Hyperuniform particle arrangements are characterized by a local number variance that grows more slowly than the volume of the observation window. We generalize this concept to describe particle systems in which particles carry weights:…

In causal models, a given mechanism is assumed to be invariant to changes of other mechanisms. While this principle has been utilized for inference in settings where the causal variables are observed, theoretical insights when the variables…

Our aim in this paper is to study the Cahn-Hilliard equation with singular potentials and dynamic boundary conditions. In particular, we prove, owing to proper approximations of the singular potential and a suitable notion of variational…

A simple conservation law formula for field equations with a scaling symmetry is presented. The formula uses adjoint-symmetries of the given field equation and directly generates all local conservation laws for any conserved quantities…

In classical extreme value theory probabilities of extreme events are estimated assuming all the components of a random vector to be in a domain of attraction of an extreme value distribution. In contrast, the conditional extreme value…

Many physical systems share the property of scale invariance. Most of them show ordinary power-law scaling, where quantities can be expressed as a leading power law times a scaling function which depends on scaling-invariant ratios of the…

We argue that conservation laws based on the local matter-only stress-energy-momentum tensor (characterized by energy and momentum per unit volume) cannot adequately explain a wide variety of even very simple physical phenomena because they…

We use the Lagrange-Noether methods to derive the conservation laws for models in which matter interacts nonminimally with the gravitational field. The nonminimal coupling function can depend arbitrarily on the gravitational field strength.…

A variety of real-world applications are modeled via hyperbolic conservation laws. To account for uncertainties or insufficient measurements, random coefficients may be incorporated. These random fields may depend discontinuously on the…

In recent years, statistical characterization of the discrete conservative dynamical systems (more precisely, paradigmatic examples of area-preserving maps such as the standard and the web maps) has been analyzed extensively and shown that,…

Are the electromagnetic scalar and vector potentials dispensable? Lev Vaidman has suggested that local interactions of gauge-invariant quantities, e.g. magnetic torques, suffice for the description of all quantum electromagnetic phenomena.…

We consider controllability for divergence-free systems that have a conserved quantity and satisfy a H\"ormander condition. It is shown that such systems are controllable, provided that the conserved quantity is a proper function. The proof…

In this paper, under some weaker conditions, we give three laws of large numbers under sublinear expectations (capacities), which extend Peng's law of large numbers under sublinear expectations in [8] and Chen's strong law of large numbers…

The dynamics of species' densities depend both on internal and external variables. Internal variables include frequencies of individuals exhibiting different phenotypes or living in different spatial locations. External variables include…

In this paper, we establish some general forms of the law of the iterated logarithm for independent random variables in a sub-linear expectation space, where the random variables are not necessarily identically distributed. Exponential…

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…

We introduce a class of non-local Lagrangians which allow for the variational derivation of non-local conser- vation laws in a self-consistent manner. The formalism developed here generalizes previous approaches, used in the context of…

In the Lagrangian framework for symmetries and conservation laws of field theories, we investigate globality properties of conserved currents associated with non-global Lagrangians admitting global Euler--Lagrange morphisms. Our approach is…