相关论文: A two-stage numerical approach for the sparse init…
Quantifying how spatial disorder affects the movement of a diffusing particle or agent is fundamental to target search studies. When diffusion occurs on a network, that is on a highly disordered environment, we lack the mathematical tools…
In this paper we analyze an optimization problem with limited observation governed by a convection--diffusion--reaction equation. Motivated by a Schur complement approach, we arrive at continuous norms that enable analysis of well-posedness…
In this paper, we study an optimal control problem for a nonlinear system of reaction-diffusion equations that constitutes a simplified and relaxed version of a thermodynamically consistent phase field model for tumor growth originally…
A singularly perturbed parabolic problem of convection-diffusion type with a discontinuous initial condition is examined. A particular complimentary error function is identified which matches the discontinuity in the initial condition. The…
We study optimal control of diffusions with slow and fast variables and address a question raised by practitioners: is it possible to first eliminate the fast variables before solving the optimal control problem and then use the optimal…
We study an optimal control problem in which both the objective function and the dynamic constraint contain an uncertain parameter. Since the distribution of this uncertain parameter is not exactly known, the objective function is taken as…
In this paper, we propose high order numerical methods to solve a 2D advection diffusion equation, in the highly oscillatory regime. We use an integrator strategy that allows the construction of arbitrary high-order schemes {leading} to an…
Reflected diffusions naturally arise in many problems from applications ranging from economics and mathematical biology to queueing theory. In this paper we consider a class of infinite time-horizon singular stochastic control problems for…
The present work proposes a second-order time splitting scheme for a linear dispersive equation with a variable advection coefficient subject to transparent boundary conditions. For its spatial discretization, a dual Petrov--Galerkin method…
We consider an advection-diffusion equation that is both non-coercive and advection-dominated. We present a possible numerical approach, to our best knowledge new, and based on the invariant measure associated to the original equation. The…
We prove convergence of the proximal policy gradient method for a class of constrained stochastic control problems with control in both the drift and diffusion of the state process. The problem requires either the running or terminal cost…
We investigate a numerical behaviour of robust deterministic optimal control problem subject to a convection diffusion equation containing uncertain inputs. Stochastic Galerkin approach, turning the original optimization problem containing…
Diffusion models have established new state of the art in a multitude of computer vision tasks, including image restoration. Diffusion-based inverse problem solvers generate reconstructions of exceptional visual quality from heavily…
The inverse problem of backward diffusion is known to be ill-posed and highly unstable. Backward diffusion processes appear naturally in image enhancement and deblurring applications. It is therefore greatly desirable to establish a…
We study the effect of the streamline upwind/Petrov Galerkin (SUPG) stabilized finite element method on the discretization of optimal control problems governed by linear advection-diffusion equations. We compare two approaches for the…
This paper is concerned with the problem of enhancing convection-cooling via active control of the incompressible velocity field, described by a stationary diffusion-convection model. This essentially leads to a bilinear optimal control…
The behaviour is investigated of solutions to a diffusion equation on the real line with nonlocal and singular reaction term, i.e., given by a Dirac source or sink at the origin. It gives a simplified representation of for example a control…
For diffusion-reaction equations employing a splitting procedure is attractive as it reduces the computational demand and facilitates a parallel implementation. Moreover, it opens up the possibility to construct second-order integrators…
We propose a general control framework for two-phase flows with variable densities in the diffuse interface formulation, where the distribution of the fluid components is described by a phase field. The flow is governed by the diffuse…
Our aim is to study the backward problem, i.e. recover the initial data from the terminal observation, of the subdiffusion with time dependent coefficients. First of all, by using the smoothing property of solution operators and a…