Related papers: A variational principle for volume-preserving dyna…
We discuss a mathematical framework for analysis of optimal control problems on infinite-dimensional manifolds. Such problems arise in study of optimization for partial differential equations with some symmetry. It is shown that some…
Spearheaded by the recent efforts to derive stochastic geophysical fluid dynamics models, we present a generic framework for introducing stochasticity into variational principles through the concept of a semi-martingale driven variational…
The Liouville theorem is a fundamental concept in understanding the properties of systems that adhere to Hamilton's equations. However, the traditional notion of the theorem may not always apply. Specifically, when the entropy gradient in…
The maximum volume principle is investigated as a means to solve the following problem: Given a set of arbitrary interpolation nodes, how to choose a set of polynomial basis functions for which the Lagrange interpolation problem is…
We establish three variational principles for the upper metric mean dimension with potential of level sets of continuous maps in terms of the entropy of partitions and Katok's entropy of the underlying system. Our results hold for dynamical…
It is shown that the geometry of locally homogeneous multisymplectic manifolds (that is, smooth manifolds equipped with a closed nondegenerate form of degree > 1, which is locally homogeneous of degree k with respect to a local Euler field)…
The variational principle and the corresponding differential equation for geodesic circles in two dimensional (pseudo)-Riemannian space are being discovered. The relationship with the physical notion of uniformly accelerated relativistic…
The Active Flux method is a finite volume method for hyperbolic conservation laws that uses both cell averages and point values as degrees of freedom. Several versions of such methods are currently under development. We focus on third order…
In this paper, we develop several related finite dimensional variational principles for discrete optimal transport (DOT), Minkowski type problems for convex polytopes and discrete Monge-Ampere equation (DMAE). A link between the discrete…
In this article, we introduce the notion of the Riemann-Liouville fractional integral of set-valued mappings via integrable selections. We establish fundamental properties of this fractional integral, including convexity, boundedness, and…
It is shown that when in a higher order variational principle one fixes fields at the boundary leaving the field derivatives unconstrained, then the variational principle (in particular the solution space) is not invariant with respect to…
This paper is devoted to the problem of classification, up to smooth isomorphisms or up to orbital equivalence, of smooth integrable vector fields on 2-dimensional surfaces, under some nondegeneracy conditions. The main continuous…
The dynamics of many natural systems is dominated by non-linear waves propagating through the medium. We show that the dynamics of non-linear wave fronts with positive surface tension can be formulated as a gradient system. The variational…
We derive the equations of nonlinear magnetoelastostatics using several variational formulations involving the mechanical deformation and an independent field representing the magnetic component. An equivalence is also discussed, modulo…
In this paper we provide an integral variational formulation for a vector play operator where the inputs are allowed to be arbitrary functions with (pointwise) bounded variation, not necessarily left or right continuous. We prove that this…
We show a novel systematic way to construct conservative finite difference schemes for quasilinear first-order system of ordinary differential equations with conserved quantities. In particular, this includes both autonomous and…
This paper aims to study the relationship between the maximum principle and the dynamic programming principle for recursive optimal control problem of stochastic evolution equations, where the control domain is not necessarily convex and…
We propose finite-volume schemes for general continuity equations which preserve positivity and global bounds that arise from saturation effects in the mobility function. In the case of gradient flows, the schemes dissipate the free energy…
Classical relativistic system of point particles coupled with an electromagnetic field is considered in the three-dimensional representation. The gauge freedom connected with the chronometrical invariance of the four-dimensional description…
Variational principles for magnetohydrodynamics (MHD) were introduced by previous authors both in Lagrangian and Eulerian form. In this paper we introduce simpler Eulerian variational principles from which all the relevant equations of…