arXiv subjects

Gabriela Marinoschi

Publications and source records attributed to Gabriela Marinoschi.

25 records · Page 2Linked to original sources

arXiv2016

Feedback stabilization of the Cahn-Hilliard type system for phase separation

This article is concerned with the internal feedback stabilization of the phase field system of Cahn-Hilliard type, modeling the phase separation in a binary mixture. Under suitable assumptions on an arbitrarily fixed stationary solution, we construct via spectral separation arguments a feedback controller having the support in an arbitrary open subset of the space domain, such that the closed loop nonlinear system exponentially reach the prescribed stationary solution. This feedback controller has a finite dimensional structure in the state space of solutions. In particular, every constant stationary solution is admissible.

math.AP↗

arXiv2015

A boundary control problem for a possibly singular phase field system with dynamic boundary conditions

This paper deals with an optimal control problem related to a phase field system of Caginalp type with a dynamic boundary condition for the temperature. The control placed in the dynamic boundary condition acts on a part of the boundary. The analysis carried out in this paper proves the existence of an optimal control for a general class of potentials, possibly singular. The study includes potentials for which the derivatives may not exist, these being replaced by well-defined subdifferentials. Under some stronger assumptions on the structure parameters and on the potentials (namely for the regular and the logarithmic case having single-valued derivatives), the first order necessary optimality conditions are derived and expressed in terms of the boundary trace of the first adjoint variable.

math.AP↗

arXiv2014

Nonlinear parabolic flows with dynamic flux on the boundary

A nonlinear divergence parabolic equation with dynamic boundary conditions of Wentzell type is studied. The existence and uniqueness of a strong solution is obtained as the limit of a finite difference scheme, in the time dependent case and via a semigroup approach in the time-invariant case.

math.AP↗

arXiv2014

Optimal control for a phase field system with a possibly singular potential

In this paper we study a distributed control problem for a phase field system of Caginalp type with logarithmic potential. The main aim of this work would be to force the location of the diffuse interface to be as close as possible to a prescribed set. However, due to the discontinuous character of the cost functional, we have to approximate it by a regular one and, in this case, we solve the associated control problem and derive the related first order necessary optimality conditions.

math.AP↗

arXiv2014

Sharp interface control in a Penrose-Fife model

In this paper we study a singular control problem for a system of PDEs describing a phase-field model of Penrose-Fife type. The main novelty of this contribution consists in the idea of forcing a sharp interface separation between the states of the system by using heat sources distributed in the domain and at the boundary. We approximate the singular cost functional with a regular one, which is based on the Legendre-Fenchel relations. Then, we obtain a regularized control problem for which we compute the first order optimality conditions using an adapted penalization technique. The proof of some convergence results and the passage to the limit in these optimality conditions lead to the characterization of the desired optimal controller.

math.AP↗

arXiv2013

Identification of a diffusion coefficient in strongly degenerate parabolic equations with interior degeneracy

We study two identification problems in relation with a strongly degenerate parabolic diffusion equation characterized by a vanishing diffusion coefficient $u\in W^{1,\infty},$ with the property $\frac{1}{u}\notin L^{1}. $ The aim is to identify $u$ from certain observations on the solution, by a technique of nonlinear optimal control with control in coefficients. The existence of a controller $u$ which is searched in $% W^{1,\infty}$ and the determination of the optimality conditions are given for homogeneous Dirichlet boundary conditions. An approximating problem further introduced allows a better characterization of the optimality conditions, due to the supplementary regularity of the approximating state and dual functions and to a convergence result. Finally, an identification problem with final time observation and homogeneous Dirichlet-Neumann boundary conditions in the state system is considered. By using more technical arguments we provide the explicit form of $u$ and its uniqueness.

math.AP↗

arXiv2013

Existence for weakly coercive nonlinear diffusion equations via a variational principle

We are concerned with the study of the well-posedness of a nonlinear diffusion equation with a monotonically increasing multivalued time-dependent nonlinearity derived from a convex continuous potential having a superlinear growth to infinity. The results in this paper state that the solution of the nonlinear equation can be retrieved as the null minimizer of an appropriate minimization problem for a convex functional involving the potential and its conjugate. This approach, inspired by the Brezis-Ekeland variational principle, provides new existence results under minimal growth and coercivity conditions.

math.AP↗