相关论文: New limiter regions for multidimensional flows
This paper introduces a simple formulation for topology optimization problems ensuring manufacturability by machining. The method distinguishes itself from existing methods by using the advection-diffusion equation with Robin boundary…
Necessary and sufficient conditions for convexity and strong convexity, respectively, of sublevel sets that are defined by finitely many real-valued $C^{1,1}$-maps are presented. A novel characterization of strongly convex sets in terms of…
This paper is the second part of our series of work to establish pointwise second-order necessary conditions for stochastic optimal controls. In this part, we consider the general cases, i.e., the control region is allowed to be nonconvex,…
This article presents a new finite element method for convection-diffusion equations by enhancing the continuous finite element space with a flux space for flux approximations that preserve the important mass conservation locally on each…
The exhaustive classification of stationary incompressible flows with constant total pressure of ideal infinitely electrically conducting fluid is given. By introduction of curvilinear coordinates based on streamlines and magnetic lines of…
The purpose of this paper is to establish the first and second order necessary conditions for stochastic optimal controls in infinite dimensions. The control system is governed by a stochastic evolution equation, in which both drift and…
A general type of mathematical argument is described, which applies to all the cases in which dynamo maintenance of a steady magnetic field by motion in a uniform density is known to be impossible. Previous work has demonstrated that…
We derive the nonlinear equations satisfied by the coefficients of linear combinations that maximize their skewness when their variance is constrained to take a specific value. In order to numerically solve these nonlinear equations we…
Using a weak convergence approach, we establish a Large Deviation Principle (LDP) for the solutions of fluid dynamic systems in two-dimensional bounded domains subjected to no-slip boundary conditions and perturbed by additive noise. Our…
We study the singular stochastic optimal control problem with model uncertainty, where the necessary conditions determined by the corresponding maximum principle are trivial. Robust integral form and pointwise second order necessary…
The classical theorems of inviscid stability have been extended for compressible flows past compliant surfaces. We consider normal modes imposed on a plane parallel compressible flow past compliant walls modelled as spring-backed plates and…
In this article, we derive first-order necessary optimality conditions for a constrained optimal control problem formulated in the Wasserstein space of probability measures. To this end, we introduce a new notion of localised metric…
We introduce the concept of a control contraction metric, extending contraction analysis to constructive nonlinear control design. We derive sufficient conditions for exponential stabilizability of all trajectories of a nonlinear control…
We introduce a general framework for enforcing local or global maximum principles in high-order space-time discretizations of a scalar hyperbolic conservation law. We begin with sufficient conditions for a space discretization to be bound…
A basic idea in optimal transport is that optimizers can be characterized through a geometric property of their support sets called cyclical monotonicity. In recent years, similar "monotonicity principles" have found applications in other…
The contributions of this technical note are twofold. Firstly, we formulate an optimization problem to obtain a linear representation of a nonlinear vector field based on a system's trajectory. We also prove that its cost function is…
We establish the global well-posedness of the free boundary problem of the viscous pressureless and almost pressureless heat conductive flows in one space dimension. In both cases, arbitrarily large but smooth initial data is considered,…
We are interested in the gradient flow of a general first order convex functional with respect to the $L^1$-topology. By means of an implicit minimization scheme, we show existence of a global limit solution, which satisfies an…
We develop and analyse finite volume methods for the Poisson problem with boundary conditions involving oblique derivatives. We design a generic framework, for finite volume discretisations of such models, in which internal fluxes are not…
In this paper, we first investigate necessary optimality conditions for problems governed by systems describing the flow of an incompressible second grade fluid. Next, we study the asymptotic behavior of the optimal solution when the…