Related papers: Boundary controllability of phase-transition regio…
This paper concerns the null controllability of the two-phase 1D Stefan problem with distributed controls. This is a free-boundary problem that models solidification or melting processes. In each phase, a parabolic equation, completed with…
In this paper we consider the one-phase Stefan problem with surface tension, set in a two-dimensional strip-like geometry, with periodic boundary conditions respect to the horizontal direction $x_1\in\mathbb{T}$. We prove that the system is…
This paper presents the control design of the two-phase Stefan problem. The two-phase Stefan problem is a representative model of liquid-solid phase transition by describing the time evolutions of the temperature profile which is divided by…
This paper deals with the exact controllability to the trajectories of the one--phase Stefan problem in one spatial dimension. This is a free-boundary problem that models solidification and melting processes. It is assumed that the physical…
We consider the inverse multiphase Stefan problem, where information on the heat flux on the fixed boundary is missing and must be found along with the temperature and free boundaries. Optimal control framework is pursued, where boundary…
In this paper, a backstepping control of the one-phase Stefan Problem, which is a 1-D diffusion Partial Differential Equation (PDE) defined on a time varying spatial domain described by an ordinary differential equation (ODE), is studied. A…
This paper presents results for the sampled-data boundary feedback control to the Stefan problem. The Stefan problem represents a liquid-solid phase change phenomenon which describes the time evolution of a material's temperature profile…
We prove that a free boundary semilinear heat equation with Stefan boundary condition and radially symmetric data is locally null controllable. The strategy involves reducing the problem to the corresponding one-dimensional formulation and…
We consider the inverse multiphase Stefan problem with homogeneous Dirichlet boundary condition on a bounded Lipschitz domain, where the density of the heat source is unknown in addition to the temperature and the phase transition…
This paper provides an observer-based event-triggered boundary control strategy for the one-phase Stefan problem using the position and velocity measurements of the moving interface. The infinite-dimensional backstepping approach is used to…
We develop a new variational formulation of the inverse Stefan problem, where information on the heat flux on the fixed boundary is missing and must be found along with the temperature and free boundary. We employ optimal control framework,…
We analyze the state constrained inverse Stefan type parabolic free boundary problem as an optimal control problem in the Sobolev-Besov spaces framework. Boundary heat flux, density of heat sources, and free boundary are components of the…
S. Hansen and E. Zuazua [SIAM J. Cont. Optim., 1995] studied the problem of exact controllability of two strings connected by a point mass with constant physical coefficients. In this paper we study the same problem with variable physical…
In the paper, the problems of controllability and approximate controllability are studied for the control system $w_t=\frac{1}{\rho}\left(kw_x\right)_x+\gamma w$, $\left.\left(\sqrt{\frac{k}{\rho}}w_x\right)\right|_{x=0}=u$, $x>0$,…
We discuss the feedback control problem for a two-dimensional two-phase Stefan problem. In our approach, we use a sharp interface representation in combination with mesh-movement to track the interface position. To attain a feedback…
We consider an optimal control problem where the state is governed by a free boundary problem called the two-phase membrane problem and the control appears in the coefficients of the characteristic function of the positivity and negativity…
This paper develops a control and estimation design for the one-phase Stefan problem. The Stefan problem represents a liquid-solid phase transition as time evolution of a temperature profile in a liquid-solid material and its moving…
Optimal control of the singular nonlinear parabolic PDE which is a distributional formulation of multidimensional and multiphase Stefan-type free boundary problem is analyzed. Approximating sequence of finite-dimensional optimal control…
We investigate a hierarchical control problem for a one-dimensional Stefan system with localized distributed controls. The setting combines a Stackelberg strategy with a Nash equilibrium among multiple followers, yielding a multi-objective…
Many metal manufacturing processes involve phase change phenomena, which include melting, boiling, and vaporization. These phenomena often occur concurrently. A prototypical 1D model for understanding the phase change phenomena is the…