Parabolic systems defined over GF(q) have been classified by Timmesfeld for q > 4 and by Stroth for q = 2 (see references). We deal with the case q = 3 . Parabolic systems have been classified by Niles, Timmesfeld, Stroth, and Heiss, if the field of definition is G F (2) or has at least four elements. [Ni, Timl, Tim2, Tim5, Tim7, Stl, St2, St3, He]. We treat the GF(3) case, where only partial r...

This paper proposes a hybrid control methodology which integrates feedback and switching for constrained stabilization of parabolic partial differential equation (PDE) systems for which the spectrum of the spatial differential operator can be partitioned into a finite slow set and an infinite stable fast complement. Galerkin’s method is initially used to derive a finite-dimensional system (set ...

We study solutions of the system of PDE Dψ(vt) = DivDF (Dv), where ψ and F are convex functions. This type of system arises in various physical models for phase transitions. We establish compactness properties of solutions that allow us to verify partial regularity when F is quadratic and characterize the large time limits of weak solutions. Special consideration is also given to systems that a...

We consider systems governed by a nonlinear parabolic equation, with a distributed control and a disturbance in the initial condition. We prove the existence of solutions to a corresponding minimax problem, and we obtain necessary optimality conditions in the form of Pontryagin’s principles.

We study degenerate quasilinear parabolic systems in two different domains, which are connected by a nonlinear transmission condition at their interface. For a large class of models, including those modeling pollution aggression on stones and chemotactic movements of bacteria, we prove global existence, uniqueness and stability of the solutions.

The aim of this paper is to point out some new results on regional boundary gradient controllability for parabolic systems. First, we give a definition and some properties of this concept, then we concentrate on the determination of the control achieving regional boundary gradient target with minimum energy and we develop an approach that leads to numerical algorithm for the computation of the ...

In this work we construct and analyse transparent boundary conditions (TBCs) for general systems of parabolic equations. These TBCs are constructed for the fully discrete scheme (θ–method, finite differences), in order to maintain unconditional stability of the scheme and to avoid numerical reflections. The discrete transparent boundary conditions (DTBCs) are discrete convolutions in time and a...

Abstract. In this paper, we investigate the numerical identifications of physical parameters in parabolic initial-boundary value problems. The identifying problem is first formulated as a constrained minimization one using the output least squares approach with the H 1-regularization or BV -regularization. Then a simple finite element method is used to approximate the constrained minimization p...

In this paper we formulate and study a minimax control problem for a class of parabolic systems with controlled Dirichlet boundary conditions and uncertain distributed perturbations under pointwise control and state constraints. We prove an existence theorem for minimax solutions and develop effective penalized procedures to approximate state constraints. Based on a careful variational analysis...