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Mohammad AKIL
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Welcome to my website! Here, you will find a comprehensive overview of my work, including summaries of my research, links to publications, my resume, and additional resources. The goal of this site is to provide easy access to the various projects and studies I’ve undertaken. If you have any inquiries or wish to discuss any topic in detail, please don't hesitate to reach out via the contact information provided at the bottom of the page.
About Me
About Me
My name is Mohammad AKIL and I am an applied mathematician. I am an expert in the control theory of Partial Differential Equations and Optimal Control. I work on the stabilization and controllability of different types of PDE's in monodimensional and multidimensional domains. Likely, (wave equations, piezoelectric material, Euler Bernoulli beam equations, Timoshenko systems, Bresse systems...). I study the energy decay rate of these systems by considering different types of dissipation law either smooth or non-smooth coefficients like (Frictional damping, Past history, Time delay, Fractional damping, Kelvin-Voigt damping, Thermoelastic law ...).
Control Theory influences the behavior of a physical system to achieve the desired goal through the use of its feedback that monitors the effect of a system and modifies its output. It is applied in a diverse range of scientific and engineering disciplines:
The reduction of noise.
The vibration of structures like seismic waves and earthquakes.
The regulation of biological systems like the human cardiovascular system.
The design of robotic systems.
Laser control in quantum mechanical and molecular systems.
I hold a PhD in applied Mathematics from University of Limoges (France) under the supervision of Pr. Noureddine IGBIDA and the Lebanese University under the supervision of Pr. Ali WEHBE. I obtained it on October 06, 2017.
In 2018-2019, I worked as temporary teaching and research assistant at the INSA de Rouen (National Institut of Sciences and Technologies)-France.
In 2020-2021 I worked as Associated Professor at University of Savoie Mont Blanc (Chambery-France).
Currently, I am an Associate Professor (Maitres de Conférences) at Universite Polytechnique Hauts de France (Valenciennes -France). .
Publications-Preprints
Published Papers:
M. Akil, Z. Brown and A. Özkan Özer, Fully Inertial SCOLE Model Involving Shear-Velocity Boundary Feedback. Applied Mathematics Letters, Volume 178, 2026. DOI
M. Akil, Z. Brown, I. Issa and A. A. Özkan Özer, Dynamic Stabilization of Serially-Connected Strings with a Dynamical Interior Mass: Unveiling the Role of Higher-Order Nodal Damping. Math. Control Signals Syst. (2026). DOI
M. Akil, Z. Brown and A. Özkan Özer, Unconditional Exponential Stability via Discontinuous Interface Control Design in Coupled wave equations with an interial boundary. IEEE Control Systems Letters, vol. 9, pp. 2897-2902, 2025. DOI
M. Akil, G. Fragnelli and A. Sbai, Degenerate/singular beam-type equations: a controllability result. Mathematical Control and Related Fields. 2026, 18: 397-432. DOI
M. Akil, G. Fragnelli and S. Ismail, Boundary observability and null-controllability for non-autonomous degenerate hyperbolic equations via energy estimates. J. Evol. Equ. 25, 93 (2025). DOI
M. Akil, M., I. Issa, A. Özkan Özer and C. Pignotti, New Stability Results for Piezoelectric Beams with a Dynamic Tip Load: Partial Damping and the Interplay of Lower- and Higher-Order Effects.Appl Math Optim 92, 23 (2025). DOI
M. Akil, A. Özkan Özer, V. Régnier and H. Saleh, More Insights into Stability Analysis of Shear-Damped Laminates: The Role of Active Boundary and Lower-Order Passive Distributed Dampers Under Various Boundary Conditions. ESAIM: COCV, 31-52(2025). DOI
M. Akil and V. Régnier, Spectrum analysis of the underlying operator for a 2d piezoelectric beam with magnetic effect on an annular domain. Math. Control Signals Syst. (2025). DOI
M. Akil, S. Nicaise, A. Özkan Özer and H. Saleh, Advancing insights into the stabilization of novel serially-connected magnetizable piezoelectric and elastic beam. SIAM Journal on Control and Optimization, 63(3), 1798–1825, 2025. DOI
M. Akil, Enhanced polynomial energy decay rate for a serially-connected magnetizable piezoelectric-elastic smart design. Evolution Equations and Control Theory, 2025 14(6): 1320-1342. DOI
M. Akil, M. Azzaoui G. Fragnelli and J. Salhi, Boundary Controllability of coupled degenrate Euler-Bernoulli beam equation. Communications on Pure and Applied Analysis (CPAA), 24(7): 1220-1241. DOI
M. Akil, G. Fragnelli and S. Ismail, Non-autonomous degenrate parabolic equations with Robin boundary conditions: Carleman estimates and null-controllability Appl Math Optim 91, 35 (2025). DOI
M. Akil, G. Fragnelli, S. Ismail and A. Özkan Özer, Exponential stabilization of an Euler-Bernoulli beam by a heat equation involving memory effects Asymptotic Analysis. 2025,141(3):157-177. DOI
M. Akil, F. Dell'Oro, G. Fragnelli , V. Régnier and A. Soufyane, Asymptotic behavior of the equivalent Timoshenko linear beam model used in the analysis of tower buildings. Z. Angew. Math. Phys. 76, 40 (2025). DOI
M. Akil, G. Fragnelli and S. Ismail. Null-controllability and Carleman estimates for non-autonomous degenerate PDEs: a climatological application, Journal of Mathematical Analysis And Applications, 543 (2025) , 128984 DOI
M. Akil, G. Fragnelli and I. Issa. Stability of degenerate wave equations with a singular potential and local damping. Discrete and Continuous Dynamical Systems - B 2025, 30(5): 1575-1606. DOI
M. Akil, G. Fragnelli, I. Issa, Stability for degenerate wave equations with drift under simultaneous degenerate damping, Journal of Differential Equations, 416 (2), 1178-1221, 2025. DOI
M. Akil, G. Fragnelli, and I. Issa, The energy decay rate of a transmission system governed by the degenerate wave equation with drift and under heat conduction with the memory effect, Math. Nachr. 297(2024), 3766–3796. DOI
M. Akil, M. Ghader, Z. Hajjej and M. Samoury, Well-posedness and Polynomial Energy Decay Rate of a Transmission Problem for Rayleigh Beam Model with Heat Conduction, Asymptotic Analysis,1 Jan. 2023 : 115 – 156. DOI
M. Akil, S. Nicaise, A. Ökan Özer and V. Régnier. Stability Results for Novel Serially-Connected Magnetizable Piezoelectric and Elastic Smart-System Designs. Appl Math Optim 89, 64 (2024). DOI
M. Akil and Z. Hajjej, Exponential stability and exact controllability of a system of coupled wave equations by second-order terms (via Laplacian) with only one non-smooth local damping, Math. Meth. Appl. Sci. 47(2024), 1883–1902, DOI
M. Akil, H. Badawi and Z. Hajjej, Stability and instability of Kirchhoff plate equations with delay on the boundary control. (2023). Electronic Journal of Differential Equations, 2023(01-87), No. 68, 1-18. DOI
M. Akil & V. Régnier. Asymptotic behaviour of a 2D Piezoelectric beam with magnetic effect on a rectangular or annular domain: Case without geometric conditions. Evolution Equations and Control Theory, 2024, 13(2): 478-509 DOI
M. Akil, A. Soufyane & Y. Belhamadia, Stabilization Results of a Piezoelectric Beams with Partial Viscous Dampings and Under Lorenz Gauge Condition. Appl Math Optim 87, 26 (2023) DOI
M. Akil, Stability of piezoelectric beam with magnetic effect under (Coleman or Pipkin)–Gurtin thermal law. Z. Angew. Math. Phys. 73, 236 (2022). DOI
M. Akil, H. Badawi, & S. Nicaise, S. Stability results of locally coupled wave equations with local Kelvin-Voigt damping: Cases when the supports of damping and coupling coefficients are disjoint. Comp. Appl. Math. 41, 240 (2022). DOI
M. Akil, H. Badawi, S. Nicaise and V. Régnier Stabilization of Coupled Wave Equations with Viscous Damping on Cylindrical and Non-regular Domains: Cases Without the Geometric Control Condition. Mediterr. J. Math. 19, 271 (2022). DOI
M. Akil, H. Badawi, S. Nicaise and A. Wehbe. Stability results on the Kirchhoff plate equation with delay terms on the dynamical boundary controls. Rev Mat Complut 36, 749–777 (2023). DOI
M. Akil, I. Issa & A. Wehbe, A N-dimensional elasticviscoelastic transmission problem with Kelvin–Voigt damping and non smooth coefficient at the interface. SeMA 80, 425–462 (2023). DOI .
M. Akil and Z. Liu Stabilization of the generalized Rao-Nakra beam by partial viscous damping. Math Meth Appl Sci. 2023; 46(2): 1479-1510. DOI
M. Akil, I. Issa and Ali Wehbe. Energy decay of some boundary coupled systems involving wave\ Euler-Bernoulli beam with one locally singular fractional Kelvin-Voigt damping. Mathematical Control and Related Fields, 2023, 13(1): 330-381. DOI
M. Akil and A. Wehbe, Indirect stability of a multidimensional coupled wave equations with one locally boundary fractional damping, Math. Nachr. 295 (2022), 2272–2300. DOI
M. Akil, H. Badawi, S. Nicaise and A. Wehbe. Stability results of coupled wave models with locally memory in a past history framework via nonsmooth coefficients on the interface. Math Meth Appl Sci. 2021; 44: 6950–6981. DOI
M. Akil, I. Issa and A. Wehbe. Stability Results of an Elastic/Viscoelastic Transmission Problem of Locally Coupled Waves with Non Smooth Coefficients. Acta Appl Math 171, 23 (2021). DOI
M. Akil, H. Badawi, S. Nicaise & A. Wehbe. On the stability of Bresse system with one discontinuous local internal Kelvin–Voigt damping on the axial force. Z. Angew. Math. Phys. 72, 126 (2021). DOI
M. Akil & H. Badawi. The influence of the physical coefficients of a Bresse system with one singular local viscous damping in the longitudinal displacement on its stabilization. Evolution Equations and Control Theory, 2022, 11(6): 1903-1928. DOI
M. Akil, H. Badawi, A. Wehbe. Stability results of a singular local interaction elastic/viscoelastic coupled wave equations with time delay. Communications on Pure and Applied Analysis, 2021, 20(9): 2991-3028. DOI
M. Akil, M. Ghader, M. & Wehbe, A. The influence of the coefficients of a system of wave equations coupled by velocities on its stabilization. SeMA 78, 287–333 (2021). DOI
M. Akil, Y. Chitour, M. Ghader and A. Wehbe Stability and Exact Controllability of a Timoshenko System with Only One Fractional Damping on the Boundary. Asymptotic Analysis, 2020, (1):221-280. DOI
M. Akil, A. Wehbe. Stabilization of multidimensional wave equation with locally boundary fractional dissipation law under geometric conditions. Mathematical Control and Related Fields, 2019, 9(1): 97-116. DOI
R. Abboud, M. Akil, C. Charcosset, H. Greige-Gerges. Interaction of glucocorticoids and progesterone derivatives with human serum albumin. Chem Phys Lipids. 2017 Oct;207(Pt B):271-278. DOI
To appear:
M. Akil, Z. Brown, I. Issa and A. A. Özkan Özer, Unlocking sharp $t^{-1/N}$ energy decay: Boundary-only control of serially connected wave networks with N-inertia generating interfaces. (To appear in IEEE- Transactions on Automatic Control).
Accepted with minor or major revisions:
Submitted:
M. Akil, Z. Brown and A. Özkan Özer, Unconditional Exponential Stabilization of a Beam-Wave Transmission System with Inertial Interface Dynamics.
M. Akil, S. Nicaise and H. Saleh, Piezoelectric beam with electrical boundary coupling: well-posedness, spectral analysis and energy decay.
M. Akil, G. Fragnelli and S. Ismail, Boundary Controllability for degenrate wave equations driven by a fully time-dependent propagation speed.
M. Akil, G. Fragnelli and A. Sbai, A stability result for a degenrate/singular beam equation.
M. Akil, G. Fragnelli and S. Ismail, On a general degenerate non-autonomous parabolic equation in non-divergence form with Dirichlet or Robin boundary conditions.
If you are interested in knowing more about these publications, please visit my Research Gate page.
Teaching
Teaching
I taught many courses after completing my PhD at different faculties (Engineering - Business- Sciences and IUT). I gave variety of courses for Licenses years and Masters in Analysis, Algebra, Linear Algebra, Numerical Analysis, Partial Differential Equations and Functional Analysis, Probability, Statistics, Mathematics for economics....
Contact me
Contact me
I am completely open to new collaborations. Please, do not hesitate to contact me if you have any questions in the areas of my expertise and/or scientific interests. Any research and professional opportunities are welcome.
Illustrations
Illustrations
Illustration of a three-layer Rao-Nakra beam consistng of two piezoelectric layers and one viscoleastic layer. The longitudinal vibrations for the piezoelectric layers (1 and 3) are subjecyed to electrical boundary control voltages $V^1(t)=-b_1v_t^1(L,t)$ and $V^3(t)=-b_3v_t^3(L,t)$, respectively, while the bending motions of the whole laminate are subject to a mechanical boundary control moment $M(t)=-b_2w_{xt}(L,t)$. This figure shows the interaction and boundary control mechanisms involved in stabilizing the laminate.
Serially-connected elastic–piezoelectric–elastic transmission system clamped at both ends. The piezoelectric material itself is an elastic material covered by electrodes at their top and bottom surfaces, and connected to an external electric circuit. As the elastic layers stretches or shrinks, the piezoelectric beam stretches or shrinks as well, and therefore, charges separate and line up in the vertical direction, and electric field (voltage) is induced in the electrodes. The overall motions on the system are considered to be only longitudinal.
This illustration depicts an Euler-Bernoulli beam occupying the domain (0,1), hinged at its left end, and free to slide at its right end. The heat equation governs the domain (1,2). At the transmission point x=1, the velocity of the beam’s deflection is matched by that of the heat, showcasing the dynamic interplay between structural mechanics
and thermal dynamics in the system.
In a serially-connected design clamped at both ends, each piezoelectric beam is also elastic. It features electrodes on its top and bottom surfaces, connected to an external electric circuit. Each outer piezoelectric beam stretches or shrinks accordingly as the elastic beam undergoes longitudinal vibrations. This mechanical deformation leads to the separation and alignment of charges in the vertical direction, inducing an electric field (voltage) in their respective electrodes.
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