Related papers: Boundary Control for Transport Equations
This paper is devoted to study boundary controllability of the Korteweg-de Vries equation posed on a finite interval, in which, because of the third-order character of the equation, three boundary conditions are required to secure the…
We show that Boundary Control method, a method for hyperbolic inverse problems, is also capable of dealing directly with certain classes of elliptic and parabolic Inverse Boundary Value Problems; thus pointing towards Boundary Control…
For a class of Bellman equations in bounded domains we prove that sub- and supersolutions whose growth at the boundary is suitably controlled must be constant. The ellipticity of the operator is assumed to degenerate at the boundary and a…
We study the controllability of a Partial Differential Equation of transport type, that arises in crowd models. We are interested in controlling it with a control being a vector field, representing a perturbation of the velocity, localized…
In this paper we study optimal control problems governed by a semilinear elliptic equation. The equation is nonmonotone due to the presence of a convection term, despite the monotonocity of the nonlinear term. The resulting operator is…
The article examines a linear-quadratic Neumann control problem that is governed by a non-coercive elliptic equation. Due to the non-self-adjoint nature of the linear control-to-state operator, it is necessary to independently study both…
A variety of boundary value problems in linear transport theory are expressed as a diffusion equation of the two-way, or forward-backward, type. In such problems boundary data are specified only on part of the boundary, which introduces…
The paper considers existence results of solution for a linear coupled system of Boltzmann transport equations and related inverse problem. The system models the evolution of three species of particles, photons, electrons and positrons.…
We study a class of infinite-dimensional singular stochastic control problems with applications in economic theory and finance. The control process linearly affects an abstract evolution equation on a suitable partially-ordered…
A numerical study of an optimal control formulation for a shape optimization problem governed by an elliptic variational inequality is performed. The shape optimization problem is reformulated as a boundary control problem in a fixed…
In this work, we study a boundary control problem for the evolutionary Navier-Stokes equations, under mixed boundary conditions, in two dimensions. The cost functional here considered is of quadratic type, depending on both state and…
In this paper we study an optimal control problem (OCP) associated to a linear elliptic equation {on a bounded domain $\Omega$}. The matrix-valued coefficients A of such systems is our control taken in L2 which in particular may comprise…
This work is devoted to the analysis of the linear Boltzmann equation in a bounded domain, in the presence of a force deriving from a potential. The collision operator is allowed to be degenerate in the following two senses: (1) the…
An optimal control problem in the space of Borel measures governed by the Poisson equation is investigated. The characteristic feature of the problem under consideration is the Tikhonov regularization term in form of the transportation…
The aim of this notes is to give a concise introduction to control theory for systems governed by stochastic partial differential equations. We shall mainly focus on controllability and optimal control problems for these systems. For the…
Consider the steady neutron transport equation in 2D convex domains with in-flow boundary condition. In this paper, we establish the diffusive limit while the boundary layers are present. Our contribution relies on a delicate decomposition…
In this paper, we consider the approximate controllability of partial differential equations with time derivatives of non-integer order via boundary control. We first show the unique existence of the solution under smooth boundary…
We study a control-constrained optimal control problem governed by a semilinear elliptic equation. The control acts in a bilinear way on the boundary, and can be interpreted as a heat transfer coefficient. A detailed study of the state…
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…
We consider the linear heat equation with a Wentzell-type boundary condition and a Dirichlet control. Such a boundary condition can be reformulated as one of dynamic type. First, we formulate the boundary controllability problem of the…