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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.


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.


Barbu V.,Octav Mayer Institute of Mathematics Romanian Academy | Rockner M.,Bielefeld University
Archive for Rational Mechanics and Analysis | Year: 2013

In this work, we introduce a new method to prove the existence and uniqueness of a variational solution to the stochastic nonlinear diffusion equation dX(t) = div[∇ X(t)/{pipe}∇ X(t){pipe}]dt + X(t)dW(t) in (0, ∞) × O, where O is a bounded and open domain in ℝN, N ≧ 1 and W(t) is a Wiener process of the form W(t) = ∑∞ k = 1μkekβk(t), ek ∈ C2(Ō) ∩ H1 0(O), and βk, k ∈ ℕ are independent Brownian motions. This is a stochastic diffusion equation with a highly singular diffusivity term. One main result established here is that for all initial conditions in L2(O), it is well posed in a class of continuous solutions to the corresponding stochastic variational inequality. Thus, one obtains a stochastic version of the (minimal) total variation flow. The new approach developed here also allows us to prove the finite time extinction of solutions in dimensions 1≦ N ≦ 3, which is another main result of this work. © 2013 Springer-Verlag Berlin Heidelberg.


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.


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.


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
European Journal of Mechanics, A/Solids | Year: 2013

We study the deformation of a chiral cylinder subjected to a prescribed thermal field in the context of the linear theory of gradient thermoelasticity. First, we investigate the effects of a thermal field which is independent of the axial coordinate. It is shown that the temperature variation produces extension, bending, torsion and a plane deformation. Then, we study the deformation of the rod when the thermal field is a polynomial of degree m in the axial coordinate. The solution is reduced to the solving of some two-dimensional problems. The method is used to solve the problem of a circular cylinder subjected to a uniform temperature field. In contrast with the case of achiral materials, a constant thermal field in an isotropic chiral cylinder produces torsional effects. © 2012 Elsevier Masson SAS. All rights reserved.


Iesan D.,Octav Mayer Institute of Mathematics Romanian Academy
International Journal of Solids and Structures | Year: 2013

This paper contains a study of the problem of torsion of chiral bars with arbitrary cross-sections in the context of the linear theory of gradient elasticity. The solution is expressed in terms of solutions of four auxiliary plane problems characterized by loads which depend only on the constitutive coefficients. It is shown that, in general, the torsion produces extension (or contraction) and bending effects. The results are used to investigate the torsion of a homogeneous circular bar. In contrast with the case of achiral circular cylinders, the torsion and extension cannot be treated independently of each other. © 2012 Elsevier Ltd. All rights reserved.


Iesan D.,Octav Mayer Institute of Mathematics Romanian Academy
Mechanics Research Communications | Year: 2014

This paper is concerned with the linear theory of gradient elasticity. The deformation of homogeneous and isotropic chiral materials subjected to concentrated body forces is investigated. First, a counterpart of the Cauchy-Kowalewski-Somigliana solution in the dynamic theory of classical elasticity is established. Then, a general solution of the field equations that is analogous to the Boussinesq-Somigliana-Galerkin solution in the classical elastostatics is presented. The results are used to derive the fundamental solutions of the displacement equations in the equilibrium theory and in the case of steady vibrations. © 2014 Elsevier Ltd.

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