相关论文: On a calculus of variations problem

This study of spatio-temporal pattern formation in an annulus is motivated by two physical problems on vastly different scales. The first is atmospheric convection in the equatorial plane between the warm surface of the Earth and the cold…

We propose a two-dimensional flow model of a viscous fluid between two close moving surfaces. We show that its asymptotic behavior, when the distance between the two surfaces tends to zero, is the same as that of the the Navier-Stokes…

This paper studies formulations of second-order elliptic partial differential equations in nondivergence form on convex domains as equivalent variational problems. The first formulation is that of Smears \& S\"uli [SIAM J.\ Numer.\ Anal.\…

Existence and regularity of minimizers for a geometric variational problem is shown. The variational integral models an energy contribution of the interface between two immiscible fluids in the presence of surfactants and includes a…

Here we review the way to build analogue spacetimes in open channel flows by looking at the flow phase diagram and the corresponding analogue experiments performed during the last years in the associated flow regimes. Thin films like the…

Unlike many deterministic PDEs, stochastic equations are not amenable to the classical variational theory of Euler-Lagrange. In this paper, we show how self-dual variational calculus leads to solutions of various stochastic partial…

In this paper, we deal with an elliptic problem with the Dirichlet boundary condition. We operate in Sobolev spaces and the main analytic tool we use is the Lax-Milgram lemma. First, we present the variational approach of the problem which…

Resistance functions for two spherical particles with the Navier slip boundary condition in general linear flows, including rigid translation, rigid rotation, and strain, at low Reynolds number are derived by the method of reflections as…

This paper is concerned with analyzing a class of fractional calculus of variations problems and their associated Euler-Lagrange (fractional differential) equations. Unlike the existing fractional calculus of variations which is based on…

This paper deals with the Sturm-Liouville problem that feature distribution potential, polynomial dependence on the spectral parameter in the first boundary condition, and analytical dependence, in the second one. We study an inverse…

This work contains an exposition of foundations of the variational calculus in fibered manifolds. The emphasis is laid on the geometric aspects of the theory. Especially functionals defined by real functions (Lagrange functions) or…

We present a numerical and partially analytical study of classical particles obeying a Langevin equation that describes diffusion on a surface modeled by a two dimensional potential. The potential may be either periodic or random. Depending…

We describe the procedure for obtaining Hamiltonian equations on a manifold with $so(k, m)$ Lie-Poisson bracket from a variational problem. This implies identification of the manifold with base of a properly constructed fiber bundle…

Within the framework of variational modelling we derive a one-phase moving boundary problem describing the motion of a semipermeable membrane enclosing a viscous liquid, driven by osmotic pressure and surface tension of the membrane. For…

A moderately thick spray can be described by a coupled system of equations consisting of the incompressible Navier-Stokes equations and the Vlasov-Boltzmann equation. We investigate this kind of mathematical model in this paper. In…

Analysing an application in liquid film dynamics, a guide for obtaining the corresponding constrained functional derivatives for constraints coupling the functional variables is given. The use of constrained derivatives makes the proper…

Energies and equilibrium equations for thin elastic plates are discussed, with emphasis on several issues pertinent to recent approaches in soft condensed matter. Consequences of choice of basis, choice of invariant strain measures, and of…

We study minimal surfaces which arise in wetting and capillarity phenomena. Using conformal coordinates, we reduce the problem to a set of coupled boundary equations for the contact line of the fluid surface, and then derive simple…

Despite the many successes of the relativistic quantum theory developed by Horwitz, et. al., certain difficulties persist in the associated covariant classical mechanics. In this paper, we explore these difficulties through an examination…

A discrete-to-continuum analysis for free-boundary problems related to crystalline films deposited on substrates is performed by $\Gamma$-convergence. The discrete model here introduced is characterized by an energy with two contributions,…