1,721,002 research outputs found
Carleman estimates for degenerate parabolic operators with applications to null controllability
No full textWe prove an estimate of Carleman type for the one dimensional heat equation
where is degenerate at . Such an estimate is derived for a special pseudo-convex weight function related to the degeneracy rate of . Then, we study the null controllability on of the semilinear degenerate parabolic equation
where is an element of subset of , and is locally Lipschitz with respect to
Control and stabilization of elastic coupled systems
No full textCette thèse est constituée de deux parties principales. Dans la première partie on traite l'observabilité et la contrôlabilité exacte internes indirectes des systèmes hyperboliques faiblement couplés et du système de Timoshenko. La deuxième partie est consacrée à l'étude de problèmes concernant la stabilisation directe du système de Bresse par des feedbacks non linéaires en utilisant la méthode des multiplicateurs et des techniques d'inégalités intégrales, et sa stabilisation indirecte seulement par deux feedbacks localement distribués au voisinage du bord en utilisant l'approche de fréquence de domaine. On traite dans cette partie aussi la stabilisation indirecte du système de Timoshenko dans le cas d'un seul feedback localement distribué au voisinage du bordThis thesis consists of two main parts. In the fi#rst part, it treats the indirect internal observability and exact controllability of a weakly coupled hyperbolic system and of the Timoshenko system. The second part is devoted to the study of problems concerning the direct stabilization of the Bresse system by non-linear feedbacks using multiplier method and integral inequality techniques, and its indirect stabilization only by two locally distributed feedbacks at the neighborhood of the boundary using the frequency domain method. Is treated in this part also the indirect stabilization of the Timoshenko system subject to a single feedback locally distributed at the neighborhood of the boundar
Piecewise multiplier method and nonlinear integral inequalities for Petrowsky equation with nonlinear dissipation
No full textInternational audienceThis work is concerned with obtention of energy decay estimates for Petrowsky equation with a nonlinear dissipation which is active only in an interior subset of the domain. We prove that the piecewise multiplier method as introduced by [20] and [22] for the wave equation can be extended to the Petrowsky equation. Moreover, we also apply some recent results by the author to obtain precise decay rate estimates for the energy, without specifying the growth of the nonlinear dissipation close to the origin by means of convex properties and nonlinear integral inequalities for the energy of the solutions
Analyse asymptotique et simulation numerique des equations de base des semiconducteurs
No full textSIGLECNRS T 62168 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc
New trends towards lower energy estimates and optimality for nonlinearly damped vibrating systems.
No full textThis work has been performed in the framework of the GDR-CNRS CONEDP 3362 and the GDRE-CNRS-INDAM project in Control of PDE's.International audienc
Comments on the highly cited article: "A new definition of fractional derivative", J. ofComp. Appl. Math. 264, DOI: 10.1016/j.cam.2014.01.002 [1] and four citing articles inthe light of quality in peer-review, scientific publishing and citations practices: How peer assessment in mathematics can fail to detect trivial paraphrases of di erentiability of afunction of the real variable - How to construct an abstract general paraphrase without innovation
No full text10.1016/j.cam.2014.01.002Mathematical analyses and comments The purpose of the present paper is to analyze and comment the contents of the highly cited article [1]. We first recall some fundamental mathematical procedures to follow, when attempting to introduce a new concept in relation to classical concepts, as in [1], and we show to what extent, these procedures are not followed in [1].We then analyse [1] through three angles of views, all based on the local inversion theorem, but with a graduallydeeper basic conceptual analysis. The three analyses explain from these three angles of views that the Definition 2.1in [1] of the fractional derivative of order α ∈ (0, 1), whenever it is defined, is a paraphrase of the classical basic definition of a differentiable function f at t > 0. For this, we show that one can associate to Definition 2.1 of [1] a linear transform Dα ∈ (0, 1) , acting on the set of real-valued functions defined on the half positivereal axisand that the α-differentiablity of f is equivalent to the classical differentiability of Dα(f). We also prove that all theextended results, theorems and examples to α-differentiable functions stated and proved in [1] are paraphrases of the corresponding classical results, theorems and examples in differential and integral calculus applied to differentiable functions.In the third angle of view, we generalize the fractional derivative as stated in Definition 2.1, to an apparentnew definition of a phi-derivative but explain how once again such a definition leads to a dead-end issue, reducing toparaphrases of the notion of differentiability, and of the subsequent results and theorems in didderential and integral calculus.The first angle of view gives right away through the elementary proposition (see Corollary 4.4): a function f hasa fractional derivative of order α ∈ (0, 1) at t > 0 if and only if this function has a classical derivative at t > 0, thatfor any t > 0, the supposed new class of functions coïncides exactly with the class of differentiable functions whenrestricted to the half strictly positive real axis. This property was already proved in [5, 6], but by a different method. Moreover, the purposes of the present paper are different. We introduce larger angles of view, which explains on the basis of the local inversion theorem, the additional factor appearing between the α-derivative at t > 0 and the usual derivative of f at t > 0, as an appropriate scaling of the original variable t and of the function f.We also show how our general abstract way to set-up definitions of phi-differentiability of a function f in our thirdangle of view, allows us to directly prove that each apparent new Definition 2.1 stated respectively in the three papers [1, 2, 3] (and in similar articles and preprints) and their subsequent properties, extended results and theorems reduce all to paraphrase the classical differentiability definition, as well as the corresponding subsequent properties, extended results and theorems in differential and integral calculus. This, using suitable function phi for each of these three Definitions 2.1.We also prove in Theorem 11.1 that Theorem 3 (resp. Theorem 3.1) stated without proof, and presented as ageneral principle in [5] (resp. in [6]) is false. For this, we give a basic counterexample, and explain in Remark 11.2 thatsuch (uncountable) counterexamples can be built.We also raise several other concerns about the new definition of fractional derivatives. In particular, we analyze the artificial breaking introduced in Definition 2.1 of [1] between the case t > 0 and the case t = 0, and its mathematical consequences : the fractional differentiability at 0 does not imply the continuity at 0. It also induces the loss of uniqueness of the solutions for Cauchy problems as stated in Example 4.1 of [1] and more generally for further examples introduced in the present paper of fractional differential equations. Note, that we also explain that it is possible, changing the underlying local C1-diffeomorphism, to have no artificial breaking at t = 0, or t = a.We also shortly present some citation and dissemination data related to [1], and raise several concerns in the light ofpeer-review and editorial processes, with respect to scientific quality and innovation in mathematics, citation practices, and publishing material. We raise questions and give some suggestions about articles or scientific productions concerned by high citation indexes, but also rapidly evolving citation indexes.</div
On the influence of the coupling on the dynamics of single-observed cascade systems of PDE's
No full textInternational audienc
Indirect Boundary Stabilization of Weakly Coupled Hyperbolic Systems
No full textPreprint paper published in 2000 : Indirect boundary stabilization of weakly coupled hyperbolic systems, Laboratoire M.M.A.S., Université deMetz, Prépublications Mathématiques, n°16/2000, pages 1-27, with the support of "La Caisse d’Épargne de Lorraine Nord"(2000)International audienceThis work is concerned with the boundary stabilization of an abstract system of two coupled second order evolution equations wherein only one of the equations is stabilized (indirect damping; see, e.g., J. Math. Anal. Appl., 173 (1993), pp. 339--358). We show that, under a condition on the operators of each equation and on the boundary feedback operator, the energy of smooth solutions of this system decays polynomially at ∞.We then apply this abstract result to several systems of partial differential equations (wave-wave systems, Kirchhoff--Petrowsky systems, and wave-Petrowsky systems
A hierarchic multi-level energy method for the control of bidiagonal and mixed n-coupled cascade systems of PDE's by a reduced number of controls
No full textInternational audienc
Asymptotic stability of wave equations with memory and frictional boundary dampings.
No full textInternational audienc
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