54 research outputs found
Corrector results for a parabolic problem with a memory effect
No full textThe aim of this paper is to provide the correctors associated to the homogenization of a parabolic problem describing the heat
transfer. The results here complete the earlier study in [Jose, Rev. Roumaine Math. Pures Appl. 54 (2009) 189–222]
on the asymptotic behaviour of a problem in a domain with two components separated by an ε-periodic interface.
The physical model established in [Carslaw and Jaeger, The Clarendon Press, Oxford (1947)] prescribes on the interface the
condition that the flux of the temperature is proportional to the jump of the temperature field, by a factor of order
εγ.
We suppose that -1 < γ ≤ 1. As far as the energies of the homogenized problems are concerned, we consider the cases
-1 < γ < 1
and γ = 1 separately. To obtain the convergence of the energies, it is necessary to impose stronger assumptions on the data.
As seen
in [Jose, Rev. Roumaine Math. Pures Appl. 54 (2009) 189–222] and [Faella and Monsurrò, Topics on Mathematics for
Smart Systems, World Sci. Publ., Hackensack, USA (2007) 107–121] (also in [Donato et al., J. Math. Pures Appl.
87 (2007) 119–143]), the case γ = 1 is more interesting because of the presence of a memory effect
in the homogenized problem
Corrector results for a parabolic problem with a memory effect
No full textThe aim of this paper is to provide the correctors associated to the homogenization of a parabolic problem describing the heat transfer. The results here complete the earlier study in [Jose, Rev. Roumaine Math. Pures Appl. 54 (2009) 189.222] on the asymptotic behaviour of a problem in a domain with two components separated by an ε-periodic interface. The physical model established in [Carslaw and Jaeger, The Clarendon Press, Oxford (1947)] prescribes on the interface the condition that the flux of the temperature is proportional to the jump of the temperature field, by a factor of order εγ. We suppose that .1 \u3c γ ≤ 1. As far as the energies of the homogenized problems are concerned, we consider the cases -1 \u3c γ \u3c 1 and γ = 1 separately. To obtain the convergence of the energies, it is necessary to impose stronger assumptions on the data. As seen in [Jose, Rev. Roumaine Math. Pures Appl. 54 (2009) 189.222] and [Faella and Monsurrò, Topics on Mathematics for Smart Systems, World Sci. Publ., Hackensack, USA (2007) 107.121] (also in [Donato et al., J. Math. Pures Appl. 87 (2007) 119.143]), the case γ = 1 is more interesting because of the presence of a memory effect in the homogenized problem. © EDP Sciences, SMAI 2010
Approximate controllability of a parabolicsystem with imperfect interfaces
No full textIn this paper, the investigation of the asymptotic behavior of the approximate control for a parabolic equation with periodic rapidly oscillating coefficients depending on a parameter γ and modeling composites with interfacial resistance was completed. The approximate control and its asymptotic behavior as ε → 0 for the case −1 \u3c γ ≤ 1was done recently in Donato & Jose (2015). The remaining case γ ≤ −1 was considered. The corrector results for the latter case given in Yang (2014) play an important role when proving this result. Following an idea introduced by Lions (1991), the approximate control is constructed as the solutions of a related transposed problem having as final data the (unique) minimum point of a suitable functional. It was then demonstrated that the control and the corresponding solution of the periodic problem converge respectively to the control and to the solution of the homogenized problem. One of the main difficulties in this study was to find the appropriate limit functionals in order to obtain the convergence results. This study addressed the problem of homogenization in the context of controllability and vice-versa, showing the interplay of two approaches in the study of partial differential equations
Asymptotic behavior of the approximate controls for parabolic equations with interfacial contact resistance
No full textInternational audienc
Approximate Controllability of a Parabolic System with Imperfect Interfaces
No full textInternational audienc
Homogenization of an Eigenvalue Problem in a Two-Component Domain with Interfacial Jump
No full textThis work concerns the asymptotic behaviour of the eigenvalues and eigenvectors of a problem posed on an ε-periodic two-component domain with an imperfect interface. We obtain characterizations of the eigenvalues and give homogenization results using the periodic unfolding method. The eigenvalues of the ε-problem converge to the corresponding eigenvalues of the limit problem, for the whole sequence. The same convergence result is obtained for the corresponding eigenspaces. The convergence for the whole sequence of the corresponding eigenvectors is achieved when the associated homogenized eigenvalue is simple
Positive equilibria of weakly reversible power law kinetic systems with linear independent interactions
No full text© 2018, The Author(s). In this paper, we extend our study of power law kinetic systems whose kinetic order vectors (which we call “interactions”) are reactant-determined (i.e. reactions with the same reactant complex have identical vectors) and are linear independent per linkage class. In particular, we consider PL-TLK systems, i.e. such whose T-matrix (the matrix with the interactions as columns indexed by the reactant complexes), when augmented with the rows of characteristic vectors of the linkage classes, has maximal column rank. Our main result states that any weakly reversible PL-TLK system has a complex balanced equilibrium. On the one hand, we consider this result as a “Higher Deficiency Theorem” for such systems since in our previous work, we derived analogues of the Deficiency Zero and the Deficiency One Theorems for mass action kinetics (MAK) systems for them, thus covering the “Low Deficiency” case. On the other hand, our result can also be viewed as a “Weak Reversibility Theorem” (WRT) in the sense that the statement “any weakly reversible system with a kinetics from the given set has a positive equilibrium” holds. According to the work of Deng et al. and more recently of Boros, such a WRT holds for MAK systems. However, we show that a WRT does not hold for two proper MAK supersets: the set PL-NIK of non-inhibitory power law kinetics (i.e. all kinetic orders are non-negative) and the set PL-FSK of factor span surjective power law kinetics (i.e. different reactants imply different interactions)
Asymptotic Analysis of a Certain Class of Semilinear Parabolic Problem with Interfacial Contact Resistance
No full textAsymptotic Analysis of a Certain Class of Semilinear Parabolic Problem with Interfacial Contact Resistance
No full text© 2017, Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia. In this paper, we consider a time-dependent semilinear parabolic problem modeling the heat diffusion in a two-component composite. The domain has an ε-periodic interface, where the flux of the temperature is proportional to the jump of the temperature field by a factor of order εγ. We determine the existence and uniqueness of the weak solution of the problem and use the periodic unfolding method to find the homogenization results
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