Lack of controllability of the heat equation with memory

We consider a model for the heat equation with memory, which has infinite propagation speed, like the standard heat equation. We prove that, in spite of this, for every T > 0 there exist square integrable initial data which cannot be steered to hit zero at time T , using square integrable controls. We show that the counterexample we present complies with the restrictions imposed by the second principle of thermodynamic

Lack of controllability of thermal systems with memory

Heat equations with memory of Gurtin-Pipkin type have controllability properties which strongly resemble those of the wave equation. Instead, recent counterexamples show that when the laplacian appears also out of the memory term, the control properties do not parallel those of the (memoryless) heat equation, in the sense that there are $L^2$-initial conditions which cannot be controlled to zero. The proof of this fact (presented in previous papers) consists in the construction of two quite special examples of systems with memory which cannot be controlled to zero. Here we prove that lack of controllability holds in general, for every systems with smooth memory kernel

On a three-dimensional and two four-dimensional oncolytic viro-therapy models

We revisit here and carry out further works on tumor-virotherapy compartmental models of [Tian, 2011, Wang et al., 2013, Phan and Tian, 2017, Guo et al., 2019]. The results of these papers are only slightly pushed further. However, what is new is the fact that we make public our electronic notebooks, since we believe that easy electronic reproducibility is crucial in an era in which the role of the software becomes very important.Comment: 41 pages, 15 figure

Embedding Domain Technique for a Fluid-Structure Interaction Problem

Part 5: Flow ControlInternational audienceWe present a weak formulation for a steady fluid-structure interaction problem using an embedding domain technique with penalization. Except of the penalizing term, the coefficients of the fluid problem are constant and independent of the deformation of the structure, which represents an advantage of this approach. A second advantage of this model is the fact that the continuity of the stress at the fluid-structure interface does not appear explicitly. Numerical results are presented

O scurtă istorie a modelării matematice a dinamicii populațiilor

auto-éditionInternational audienceAceastă carte urmărește istoria dinamicii populațiilor--un domeniu teoretic strâns legat de genetică, ecologie, epidemiologie și demografie--la care matematica a adus contribuții semnificative. Sunt trecute în revistă o diversitate de subiecte importante: creșterea exponențială, de la Euler și Malthus la politica chineză a copilului unic; dezvoltarea modelelor stocastice, de la legile lui Mendel și problema extincției numelor de familie la teoria percolației pentru răspândirea epidemiilor; populațiile haotice, unde determinismul și șansa se întrepătrund

Fixed Domain Algorithms in Shape Optimization for Stationary Navier-Stokes Equations

Part 6: Shape and Structural OptimizationInternational audienceThe paper aims to illustrate the algorithm developed in the paper [6] in some specific problems of shape optimization issued from fluid mechanics. Using the fictitious domain method with penalization, the fluid equations will be solved in a fixed domain. The admissible shapes are parametrized by continuous function defined in the fixed domain, then the shape optimization problem becomes an optimal control problem, where the control is the parametrization of the shape. We get the directional derivative of the cost function by solving co-state equation. Numerical results are obtained using a gradient type algorithm