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Munteanu I.,Octav Mayer Institute of Mathematics Romanian Academy | Munteanu I.,Al. I. Cuza University
Systems and Control Letters | Year: 2013

We study 2D (and 3D) incompressible magnetohydrodynamic (MHD) channel flow, also known as Hartmann's flow, which is electrically conducting and subject to an external transverse magnetic field. We consider periodic boundary conditions along one axis (two axes, for the three-dimensional case). We consider the flow at low magnetic Reynolds number and obtain the so-called simplified magnetohydrodynamic (SMHD) equations. We stabilize the linearized SMHD system by using a boundary finite-dimensional feedback controller with vertical velocity observation which acts only on the normal component of the velocity field. The stability is achieved without any a priori condition on the viscosity coefficient, that is, on the Reynolds number. © 2012 Elsevier B.V. All rights reserved.


Munteanu I.,Octav Mayer Institute of Mathematics Romanian Academy | Munteanu I.,Al. I. Cuza University
Numerical Functional Analysis and Optimization | Year: 2012

We present an extension from two dimensions to three dimensions of a boundary control law, which stabilizes the parabolic profile of an infinite channel flow. The controller acts on the normal component of the velocity only. The stability is achieved without any a priori condition on the viscosity coefficient, that is on Reynolds number. © 2012 Copyright Taylor and Francis Group, LLC.


Iesan D.,Octav Mayer Institute of Mathematics Romanian Academy | Quintanilla R.,Polytechnic University of Catalonia
International Journal of Thermal Sciences | Year: 2012

This paper is concerned with the linear theory of heat conduction in continua with microtemperatures. The work is motivated by increasing use of materials which possess thermal variation at a microstructure level. The theory of plane thermal fields in homogeneous and isotropic bodies is investigated. The first part of the paper is devoted to the basic boundary value problems of the stationary theory. The fundamental solutions of the field equations are established and the potentials of single layer and double layer are introduced. The boundary value problems are reduced to the study of singular integral equations for which Fredholm's theorems hold. Existence and uniqueness results are established. The second part of the paper is devoted to time-dependent problems. First, a solution of Galerkin type of field equations is established. Then a uniqueness theorem and an instability result are presented. The solution of Galerkin type is used to investigate the effects of some concentrated heat sources acting in an infinite medium. The theory is applied to solve the problem of stationary thermal fields in a hollow cylinder. © 2012 Elsevier Masson SAS. All rights reserved.


Carja O.,Al. I. Cuza University | Carja O.,Octav Mayer Institute of Mathematics Romanian Academy | Donchev T.,Al. I. Cuza University | Postolache V.,Al. I. Cuza University
Journal of Dynamical and Control Systems | Year: 2013

In a Banach space X with uniformly convex dual, we study the evolution inclusion of the form x'(t) ε Ax(t)+F(x(t)), where A is an m-dissipative operator and F is an upper hemicontinuous multifunction with nonempty convex and weakly compact values. If X* is uniformly convex and F is one-sided Perron with sublinear growth, then, we prove a variant of the well known Filippov-PliŚ theorem. Afterward, sufficient conditions for near viability and (strong) invariance of a set K⊆̄D(A) are established. As applications, we derive ε - δ lower semicontinuity of the solution map and, consequently, the propagation of continuity of the minimum time function associated with the null controllability problem. © 2013 Springer Science+Business Media New York.


Iesan D.,Octav Mayer Institute of Mathematics Romanian Academy | Quintanilla R.,Polytechnic University of Catalonia
International Journal of Non-Linear Mechanics | Year: 2013

This paper is concerned with the non-linear theory of porous elastic bodies. First, we present the basic equations in general curvilinear coordinates. The constitutive equations for porous elastic bodies with incompressible matrix material are derived. Then, the equilibrium theory is investigated. An existence result within the one-dimensional theory is presented. The theory is applied in order to study the torsion of an isotropic circular cylinder and the flexure of a cuboid made of an anisotropic material. It is shown that the equations of equilibrium reduce to a single ordinary differential equation governing an unknown function which characterizes the aforementioned deformations. © 2012 Elsevier Ltd.

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