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AbstractsFarid AMMAR-KHODJA, University of Franche-Comté, France Title: The moment method and controllability of parabolic systems Abstract: In most of the long list of articles using the moment method to solve control problems, starting with the paper of Fattorini-Russell in the If
The aim of this talk is to show, in a first step, how this moment method works to solve the null controllability problem for the heat equation:
where
Here
In a second step, the method is extended to some particular parabolic systems for which the moment method gives a solution of the null-controllability problem seeming difficult to get by using global Carleman inequalities.
The third step is devoted to some open abstract problems. ----------------------------------------------------------------------------------------------------------------------------- Kaïs AMMARI, University of Monastir, Tunisia Title: Stability of some thermoelastic delayed systems Abstract: In this presentation, we address a stabilization problem for a generalized thermoelastic system with delay, commonly referred to as the ----------------------------------------------------------------------------------------------------------------------------- Abdes Samed BERNOUSSI, Abdelmalek Essaâdi University, Morocco Title: Estimation of unknown action for a localized system: Application to the estimation of used water in irrigation Abstract: In this work, we consider the problem of estimating an unknown action for finite-dimensional dynamical linear systems. In added, we assume that the initial state is also unknown. This problem is different from the source detection problem addressed in many previous research works. As an application, we consider the case of irrigation billing: The problem is how to estimate the used water for irrigation and the yield. Indeed, due to climate change, the lack of precipitation forces farmers to resort to water and fertilizer-intensive methods to maximize their yield. Thus, in this work, we address the problem of irrigation water billing for given crops over large areas by considering the problem of estimating an unknown action on a localized system from measurements taken during a specific time interval. We formulate the problem as an optimal control problem. As we assume that the initial state is unknown, we seek to determine the solution that minimizes, on the one hand, the value of this initial state, and on the other hand, the quantity of water required for the irrigation process. This permit to estimate the minimum of used water for irrigation and consequently permit the billing without excess. To illustrate our approach, some examples and simulation are given. ----------------------------------------------------------------------------------------------------------------------------- Idriss BOUTAAYAMOU, Ibn Zohr University, Morocco Title: Null controllability of an ODE-heat system with coupled boundary and internal terms Abstract: This talk is devoted to the null controllability of a coupled ODE-heat system internally and at the boundary with Neumann boundary control. First, we establish the null controllability of the ODE-heat with distributed control using Carleman estimates. Then, we conclude by the strategy of space domain extension. Finally, we illustrate the analysis with some numerical experiments. ----------------------------------------------------------------------------------------------------------------------------- Anna DOUBOVA, University of Seville, Spain Title: Inverse problems for 1d fluid-solid interaction model Abstract: In this talk we consider inverse problems for the partial differential equations describing the behavior of certain fluids. Our focus will be on the fluid-structure interaction problem and the objective is to determine the moving domain where the equations are satisfied, based on external measurements. We concentrate on a one-dimensional fluid-solid interaction problem for the Burgers equation, and we will prove uniqueness and conditional stability results. This work is in collaboration with J. Apraiz, E. Fernandez-Cara and M. Yamamoto [1]. [1] J. Apraiz, A. Doubova, E. Fernandez-Cara, M. Yamamoto, “Inverse problems for one-dimensional fluid-solid interaction models”, Communications on Applied Mathematics and Computation, https://doi.org/10.1007/s42967-024-00437-3 ----------------------------------------------------------------------------------------------------------------------------- Abdeladim EL AKRI, University Mohammed VI Polytechnic, Morocco Title: Auxiliary Splines Space Preconditioning for B-Splines Finite Elements: The case of Abstract: This talk presents a study of large linear systems resulting from the regular
 -splines finite element discretization of the  and  elliptic problems on unit square/cube domains. We consider systems subject to both homogeneous essential and natural boundary conditions. Our objective is to develop a preconditioning strategy that is optimal and robust, based on the Auxiliary Space Preconditioning method proposed by Hiptmair et al. [2]. Our approach is demonstrated to be robust with respect to mesh size, and we also show how it can be combined with the Generalized Locally Toeplitz (GLT) sequences analysis presented in [3] to derive an algorithm that is optimal and stable with respect to spline degree. Numerical tests are conducted to illustrate the effectiveness of our approach.References
[1] A. El Akri, K.Jbilou and A. Ratnani, Auxiliary Splines Space Preconditioning for B-Splines Finite Elements: The case of
 "\boldsymbol{H}(\mathbf{curl},\Omega)") and  "\boldsymbol{H}(div, \Omega)") elliptic problems, CAMWA 159, 102-121, (2024).[2] R. Hiptmair and J. Xu, Nodal auxiliary space preconditioning in h (curl) and h (div) spaces, SIAM Journal on Numerical Analysis 45, 2483-2509, (2007). [3] M. Mazza, C. Manni, A. Ratnani, S. Serra-Capizzano, and H. Speleers, Isogeometric analysis for 2 d and 3 d curl-div problems: Spectral symbols and fast iterative solvers, Computer Methods in Applied Mechanics and Engineering 344, 970-997, (2019). ----------------------------------------------------------------------------------------------------------------------------- Mohamed ERRAOUI, University of Chouaïb Doukkali, Morocco Title: Cameron-Martin Formula for a Class of non-Gaussian Measures Abstract: In this paper, we study the quasi-invariant property of a class of non-Gaussian measures. These measures are associated with the family of generalized grey Brownian motions. We identify the Cameron-Martin space and derive the explicit Radon-Nikodym density in terms of the Wiener integral with respect to the fractional Brownian motion. Moreover, we show an integration by parts formula for the derivative operator in the directions of the Cameron-Martin space. As a consequence, we derive the closability of both the derivative and the corresponding gradient operators. ----------------------------------------------------------------------------------------------------------------------------- Genni FRAGNELLI, University of Siena, Italy Title: Non-autonomous wave equations: a controllability result Abstract: We consider a non-autonomous wave equation on ----------------------------------------------------------------------------------------------------------------------------- Said HADD, Ibn Zohr University, Morocco Title: New results on maximal Abstract: The aim of this talk is twofold. A novel variation of the constants formula will be presented for the mild solutions of integrodifferential equations in Banach spaces by employing a perturbation semigroup approach and admissible observation operators. Subsequently, utilizing this formula, an examination of the maximal regularity for such equations is conducted by applying the sum operator method established by Da Prato and Grisvard. Importantly, it is demonstrated that the maximal ----------------------------------------------------------------------------------------------------------------------------- Moulay Lhassan HBID, University Mohammed VI Polytechnic, Morocco Title: Dynamic Systems and Population Dynamics Four Decades of Collaboration with Hammadi Bouslous Abstract: In this presentation, I will provide a retrospective of the mathematical results I have ----------------------------------------------------------------------------------------------------------------------------- Salem NAFIRI, Hassania School of Public Works, Morocco Title: Error Analysis of Physics-Informed Neural Networks for Parabolic Problems with Dynamic Boundary Conditions Abstract: Physics-Informed Neural Networks (PINNs) are deep learning-based methods designed to approximate solutions of partial differential equations (PDEs) by minimizing specific residuals mapping. In this talk, we present an error analysis estimation of PINNs for solving parabolic PDEs with dynamic boundary conditions. Numerical simulations are also conducted to validate our theoretical findings, demonstrating strong agreement with our theory. ----------------------------------------------------------------------------------------------------------------------------- Rainer Nagel, University of Tübingen, Germany Title: AGFA: from Tübingen to Marrakesh Abstract: ----------------------------------------------------------------------------------------------------------------------------- El Maati OUHABAZ, University of Bordeaux, France Title: The diamagnetic inequality for the Dirichlet-to-Neumann operator Abstract: Let If both operator are subject to Dirichlet or Neumann boundary conditions then the diamagnetic inequality says that the semigroup of ----------------------------------------------------------------------------------------------------------------------------- Mohamed OUZAHRA, Sidi Mohamed Ben Abdellah University, Morocco Title: Finite-time stabilization of linear and bilinear systems Abstract: Stability plays a fundamental role in ensuring the performance of dynamical ----------------------------------------------------------------------------------------------------------------------------- Ahmed RATNANI, University Mohammed VI Polytechnic, Morocco Title: Optimal Transport and IsoGeometric Analysis Abstract: ----------------------------------------------------------------------------------------------------------------------------- Abdelaziz RHANDI, University of Salerno, Italy Title: Impact of Mixed Boundary Conditions on Stochastic Equations with Noise at the Boundary Abstract: In this talk, we study evolution equations that are perturbed at the boundary by both noise and an unbounded perturbation. First, using the theory of regular linear systems, we prove the existence of solutions to this equation. Second, we investigate the long-time behavior of the solutions, such as the absolute continuity and the existence of an invariant measure. ----------------------------------------------------------------------------------------------------------------------------- Roland SCHNAUBELT, Karlsruhe Institute of Technology, Germany Title: Decay properties of the Maxwell system with conductivity Abstract: We discuss the linear autonomous Maxwell system with damping caused by a nonnegative conductivity ----------------------------------------------------------------------------------------------------------------------------- Mohamed Aziz TAOUDI, Cadi Ayyad University Title: Order, Topology and Fixed points: New Theoretical Insights and Applications Abstract: In this talk, we present a series of fixed point theorems developed within the framework of partially ordered topological spaces. A key focus of our work is on cases where the topology is induced by a metric. Our findings generalize several well known results in the literature, significantly expanding the scope of fixed point theory to more general settings. Throughout our analysis, we provide fresh insights into the interplay between order structures and topological properties, shedding light on previously unexplored connections. To demonstrate the practical relevance and theoretical significance of our results, we include a variety of illustrative examples and applications. The contributions presented in this talk pave the way for further research, opening new avenues for exploration in this dynamic area of mathematics. ----------------------------------------------------------------------------------------------------------------------------- Moulay Hicham TBER, Cadi Ayyad University Title: A Mixed Finite Element Method for Free Boundary Convection-Diffusion Problems Abstract: This talk will focus on time-dependent free boundary problems governed by a convectiondiffusion operator. We develop a new computational methodology that integrates a Lagrangian technique [1] with mixed finite elements, ensuring mass conservation and leading to a symmetric saddle point system with complementarity conditions [2]. A key contribution is the development of an efficient active-set solver with a Schur-complement technique. We will discuss the efficiency and accuracy of our approach and its applications in solving convection-dominated free boundary problems in finance [3] and tribology [4]. References ----------------------------------------------------------------------------------------------------------------------------- Enrique ZUAZUA, Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany Title: Modelling, Machine Learning and Control Abstract: Often in applications the first and major challenge is to derive reliable models to later employ them for design, control and decision-making purposes. In this lecture we will present a hybrid strategy, based on the combination of classical PDE approaches and data-driven ones, to design models that are both, data aware and consistent with mechanics. The appropriate blending of Machine Learning and Control techniques will play a major role. |
s until the review book of Avdonin-Ivanov, only finite dimensional controls are considered. In some particular cases, this leads to solve a basic moment problem of the form:%09%5Cin%09%5Cell%5E2,%09%5Cexists%09?%09u%09%5Cin%09L%5E2(0,%09T),%09%5Cint%5F0%5ET%09e%5E{-%5Clambda%5Fk%09t}%09u(t)%09d%09t=m%5Fk,%09k%09%5Cgeq%091. "\forall\left(m_k\right) \in \ell^2, \exists ? u \in L^2(0, T), \int_0^T e^{-\lambda_k t} u(t) d t=m_k, k \geq 1.")
%09%5Csubset(0,%09%5Cinfty) "\left(\lambda_k\right) \subset(0, \infty)")
, a necessary condition is that  "\left(e^{-\lambda_k t}\right)")
admits a biorthogonal family and this condition itself is equivalent to 
. This is a strong limitation.
is a sufficiently smooth bounded domain, 
is an open set. In this case, the associated moment problem writes: find  "u \in L^2\left(Q_T\right)")
such that%09u(t,%09x)%09d%09x%09d%09t=-e%5E{-%5Clambda%5Fk%09T}%09%5Cint%5F{%5COmega}%09y%5E0(x)%09%5Cvarphi%5Fk(x)%09d%09x,%09k%09%5Cgeq%091. "\int_0^T \int_\omega e^{-\lambda_k t} \varphi_k(x) u(t, x) d x d t=-e^{-\lambda_k T} \int_{\Omega} y^0(x) \varphi_k(x) d x, k \geq 1.")
%5F{k%09%5Cgeq%091} "\left(-\lambda_k, \varphi_k\right)_{k \geq 1}")
are the spectral elements of the Dirichlet Laplacian defined on  "L^2(\Omega)")
with domain (%5COmega) "\left(H^2 \cap H_0^1\right)(\Omega)")
. A biorthogonal family  "\left(q_k\right)")
to  "\left(e^{-\lambda_k t} \varphi_k\right)")
is constructed in %09%5Ctimes%09%5Comega) "L^2((0, T) \times \omega)")
with estimates on the norms %09%5Ctimes%09%5Comega)} "\left\|q_k\right\|_{L^2((0, T) \times \omega)}")
.
system. Thermoelastic systems describe the interaction between mechanical deformations and thermal effects in elastic materials, and the inclusion of delay terms introduces additional challenges in the analysis of their stability. Delays in such systems can arise from physical phenomena such as heat conduction or time lags in control mechanisms, making them particularly relevant in practical applications. To analyze this system, we first establish its well-posedness by utilizing the semigroup approach. Specifically, we show that the 
-semigroup, ensuring the existence, uniqueness, and continuous dependence of the solutions on the initial data. Next, we turn to the stability analysis, focusing on both exponential and polynomial stability under certain conditions. By employing a frequency-domain approach, we derive conditions that ensure the system's response diminishes over time, either at an exponential rate or at a polynomial rate. Finally, we illustrate these theoretical results by applying them to specific examples within the field of thermoelasticity. These examples highlight the practical implications of the stabilization techniques and demonstrate how the results can be applied to real systems. "\boldsymbol{H}(\mathbf{curl}, \Omega)")
and  "(0,1)")
with degeneracy at 
. Obviously, the presence of a non-autonomous term and of a degenerate function leads us to use different spaces with respect to the standard ones and it gives rise to some new difficulties. However, thanks to some suitable assumptions on the functions, one can prove some estimates on the associated energy that are crucial to prove the controllability at a fixed time 
.
-regularity of a class of integrodifferential equations
be an open subset of 
for some 
and consider two elliptic operators  "L_0 = - \sum_{k,l=1}^d \partial_k ( a_{kl} \partial_l . )")
and %09(%09a%5F{kl}%09(%5Cpartial%5Fl%09-i%09a%5Fl)%09.%09) "L_a = - \sum_{k,l=1}^d (\partial_k -i a_k) ( a_{kl} (\partial_l -i a_l) . )")
. This property, mainly known when 
, plays an important role in spectral theory of Schrödinger operators with magnetic fields. We prove a new diamagnetic inequality for the corresponding Dirichlet-to-Neumann operators on the the boundary of 
. For the scalar wave equation it is well known that the location of the support of 
and permeability 
are constant. This fact follows from a resolvent estimate which is shown by means of the eigenfunctions of the undamped Maxwell problem. We further look at the Maxwell system with matrix-valued | Online user: 2 | Privacy | Accessibility |
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