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In this paper, we propose a new policy iteration algorithm to compute the value function and the optimal controls of continuous time stochastic control problems. The algorithm relies on successive approximations using linear-quadratic…
Previous studies have identified potential instabilities in self-interacting vector theories associated with the breakdown of the well-posedness of the initial-value problem. However, these conclusions are restricted to Abelian vector…
This article proves the completeness of an axiomatization for initial value problems (IVPs) with compact initial conditions and compact time horizons for bounded open safety, open liveness and existence properties. Completeness…
The paper is devoted to the study of a new class of optimal control problems for nonsmooth dynamical systems governed by nonconvex discontinuous differential inclusions of the sweeping type with involving variable time into optimization. We…
Although many real-world stochastic planning problems are more naturally formulated by hybrid models with both discrete and continuous variables, current state-of-the-art methods cannot adequately address these problems. We present the…
We consider locally stabilized, conforming finite element schemes on completely unstructured simplicial space-time meshes for the numerical solution of parabolic initial-boundary value problems with variable, possibly discontinuous in space…
In this paper, we study the initial-boundary value problem of the Navier-Stokes system in the half space. We prove the unique solvability of the weak solution on some short time interval (0, T) with the velocity in $C^{\alpha, \frac12…
The classical Dynamic Programming (DP) approach to optimal control problems is based on the characterization of the value function as the unique viscosity solution of a Hamilton-Jacobi-Bellman (HJB) equation. The DP scheme for the numerical…
We propose a novel early-terminating mesh refinement strategy using an integrated residual method to solve dynamic feasibility problems. As a generalization of direct collocation, the integrated residual method is used to approximate an…
We present a novel structure-preserving semi-implicit finite volume method on vertex-based staggered meshes for the compatible discretization of first order systems of time-dependent partial differential equations (PDEs). The method…
This paper is dedicated to investigating the existence of solutions to the initial value problem (IVP) for a coupled system of $\Psi$-Hilfer hybrid fractional differential equations (FDEs) and boundary value problem (BVP) for a coupled…
The initial-boundary value problem (ibvp) for the $m$-th order dispersion Korteweg-de Vries (KdV) equation on the half-line with rough data and solution in restricted Bourgain spaces is studied using the Fokas Unified Transform Method…
We employ Maxwell's equations formulated in Space-Time Algebra to perform discretization of moving geometries directly in space-time. All the derivations are carried out without any non-relativistic assumptions, thus the application area of…
We consider the optimal control problem of a general nonlinear spatio-temporal system described by Partial Differential Equations (PDEs). Theory and algorithms for control of spatio-temporal systems are of rising interest among the…
In this paper we discuss the controllability of two-point boundary value problem (TBVP) for one-dimensional wave equation. Some new concepts are introduced: TBVP input control problem, minimum-input solution (MS) and pre-minimum-input…
We prove that to each initial datum in a set of positive measure in phase space, there exist uncountably-many associated weak solutions of Newton's equations of motion which govern the dynamics of two non-spherical sets with real-analytic…
In this paper we consider an initial-boundary value problem with a Caputo time derivative of order $\alpha\in(0,1)$. The solution typically exhibits a weak singularity near the initial time and this causes a reduction in the orders of…
Well-conditioned boundary integral methods for the solution of elliptic boundary value problems (BVPs) are powerful tools for static and dynamic physical simulations. When there are many close-to-touching boundaries (eg, in complex fluids)…
The use of boundary integral equations in modeling boundary value problems-such as elastic, acoustic, or electromagnetic ones-is well established in the literature and widespread in practical applications. These equations are typically…
When a numerical simulation has to handle a physics problem with a wide range of time-dependent length scales, dynamically adaptive discretizations can be the method of choice. We present a major upgrade to the numerical relativity code…