Accueil
Yavar KIAN
Maître de conférences, Centre de Physique Théorique (CPT), UMR-7332
Campus de Luminy, Case 907
13288 Marseille cedex 9, France
Tel : 04 91 26 95 29
CV: voir ici
Thèmes de recherche
Mes principaux thèmes de recherche sont:
- Problèmes inverses consistant à déterminer des coefficients dépendant du temps ou du temps et de l'espace pour différentes équations aux dérivées partielles d'évolution (Schrödinger, hyperbolique, parabolique).
- Problèmes inverses et directs pour des équations de diffusion fractionnaire en temps.
- Problème de Calderón sur un domaine non-borné.
- Problèmes inverses spectraux.
- Problèmes inverses pour des équations aux dérivées partielles non-linéaires.
- Problèmes inverses pour différentes équations aux dérivées partielles d'évolution (Schrödinger, hyperbolique) sur un guide d'ondes.
- Problèmes inverses de sources
- Problèmes inverses pour des équations aux dérivées partielles et problèmes inverses spectraux sur des variétés riemanniennes.
- Estimations (estimations dispersives et estimations de Strichartz) et étude du comportement asymptotique par rapport au temps de solutions des équations des ondes avec la présence de perturbations, dépendantes du temps et de l'espace.
Mots-clés: Problèmes inverses, équation des ondes, équation de Schrödinger, équation de la chaleur, équations elliptiques, équations de diffusion fractionnaires en temps, estimation de Carleman, problème de Calderón, problèmes inverses spectraux, estimation de stabilité pour des problèmes inverses, estimations de Strichartz locales et globales.
Publications et prépublications
Détermination de coefficients dépendant du temps pour des équations d'évolution de type hyperbolique, parabolique et Schrödinger
1) Stability of the determination of a time-dependent coefficient in parabolic equations, (with Mourad Choulli), MCRF, 3 (2013), 143-160. pdf
2) A stability result for a time-dependent potential in a cylindrical domain, (with Patricia Gaitan), Inverse Problems, 29 (2013), 065006.
3) Stable Determination of Time-Dependent Scalar Potential From Boundary Measurements in a Periodic Quantum Waveguide, (with Mourad Choulli and Eric Soccorsi) , SIAM J.Math. Anal., 47 (6) (2015), 4536-4558. pdf
4) Stable Determination of Time-Dependent Scalar Potential From Boundary Measurements in a Periodic Quantum Waveguide, (with Mourad Choulli and Eric Soccorsi) , New Prospects in Direct, Inverse and Control Problems for Evolution Equations, A. Favini, G. Fragnelli and R. M. Mininni (Eds), Springer-INdAM, Roma, 2014, 93-105.
5) Unique determination of a time-dependent coefficient from partial data, Annales de l'IHP (C) Analyse non linéaire, 34 (2017), 973-990. pdf
6) Stability in the determination of a time-dependent coefficient for wave equations from partial data, Journal of Mathematical Analysis and Applications, 436 (2016), 408-428. pdf
7) Recovery of time-dependent damping coefficients and potentials appearing in wave equations from partial data, SIAM J. Math. Anal., 48(6) (2016), 4021-4046. pdf
8) Logarithmic stability in determining the time-dependent zero order coefficient in a parabolic equation from a partial Dirichlet-to-Neumann map. Application to the determination of a nonlinear term, (with Mourad Choulli), J. Math. Pures Appl., 114 (2018),235-261. pdf
9) Recovery of time-dependent coefficient on Riemannian manifold for hyperbolic equations, (with Lauri Oksanen), to appear in IMRN, (2016). pdf
10) Hölder stably determining the time-dependent electromagnetic potential of the Schrödinger equation, (with Eric Soccorsi), to appear in SIAM J.Math. Anal., (2016). pdf
11) Determination of singular time-dependent coefficients for wave equations from full and partial data, (with Ganghui Hu), Inverse Probl. Imaging, 12 (2018), 745-772. pdf
12) Determination of convection terms and quasi-linearities appearing in diffusion equations, (with Pedro Caro), preprint, (2018). pdf
13) Recovery of time dependent coefficients from boundary data for hyperbolic equations, (with Ali Feizmohammadi, Joonas Ilmavirta, Lauri Oksanen), preprint, (2019). pdf
14) Hölder Stable Recovery of Time-Dependent Electromagnetic Potentials Appearing in a Dynamical Anisotropic Schrödinger Equation, (with Alexander Tetlow), preprint, (2019). pdf
15) Recovery of non-smooth coefficients appearing in anisotropic wave equations, (with Ali Feizmohammadi), preprint, (2019). pdf
Problèmes inverse pour des équations non-linéaires
8) Logarithmic stability in determining the time-dependent zero order coefficient in a parabolic equation from a partial Dirichlet-to-Neumann map. Application to the determination of a nonlinear term, (with Mourad Choulli), J. Math. Pures Appl., 114 (2018),235-261. pdf
12) Determination of convection terms and quasi-linearities appearing in diffusion equations, (with Pedro Caro), preprint. pdf
16) On the determination of nonlinear terms appearing in semilinear hyperbolic equations, preprint, (2018). pdf
Équations de diffusion fractionnaire en temps
17) On existence and uniqueness of solutions for semilinear fractional wave equations, (with Masahiro Yamamoto) Fractional Calculus and Applied Analysis, 20 (2017), 117-138. pdf
18) Global uniqueness in an inverse problem for time fractional diffusion equations, (with Lauri Oksanen, Eric Soccorsi, Masahiro Yamamoto), Journal of Differential Equations, 264 (2018), 1146-1170. pdf
19) On time-fractional diffusion equations with space-dependent variable order, (with Eric Soccorsi and Masahiro Yamamoto), Annales Henri Poincaré, 19 (2018), 3855-3881. pdf
20) Initial-boundary value problem for distributed order time-fractional diffusion equations, (with Zhiyuan Li, Eric Soccorsi), preprint, (2017). pdf
21) Asymptotic estimates of solutions to time-fractional diffusion equations with space-dependent variable order, (with Diomba Sambou, Eric Soccorsi), preprint, (2019). pdf
Problèmes inverses spectraux
22) Heat trace asymptotics and compactness of isospectral potentials for the Dirichlet Laplacian, (with Mourad Choulli, Laurent Kayser and Eric Soccorsi), Asymptotic Analysis, 92 (2015), 259–278. pdf
23) Uniqueness and stability results for an inverse spectral problem in a periodic waveguide, (with Otared Kavian and Eric Soccorsi) , J. Math. Pures Appl., 104 (2015), 1160-1189. pdf
24) A multidimensional Borg-Levinson theorem for magnetic Schrödinger operators with partial spectral data, Journal of Spectral Theory, 8 (2018), 235–269. pdf
25) A Borg-Levinson theorem for magnetic Schrödinger operators on a Riemannian manifold, (with M. Bellassoued, M. Choulli, D. D. Feirrera, P. Stefanov), preprint, (2018). pdf
Problèmes inverses utilisant la méthode du contrôle aux bords
26) Application of the boundary control method to partial data Borg-Levinson inverse spectral problem, (with Morgan Morancey and Lauri Oksanen), (2017), to appear in MCRF. pdf
27) Hyperbolic inverse problem with data on disjoint sets, (with Yaroslav Kurylev, Matti Lassas and Lauri Oksanen), (2018), to appear in Journal of Differential Equations, (2018). pdf
Problème de Calderón
28) Double logarithmic stability estimate in the identification of a scalar potential by a partial elliptic Dirichlet-to-Neumann map, (with Mourad Choulli and Eric Soccorsi), In memory of Alfredo Lorenzi, Bulletin SUSU MMCS, 8 (3) (2015), 78-94. pdf
29) Stability result for elliptic inverse periodic coefficient problem by partial Dirichlet-to-Neumann map, (with Mourad Choulli, Eric Soccorsi), Journal of Spectral Theory, 8 (2) (2018), 733-768. pdf
30) On the Calderon problem in periodic cylindrical domain with partial Dirichlet and Neumann data, (with Mourad Choulli, Eric Soccorsi), Mathematical Methods in the Applied Sciences, 40 (2017), 5959–5974. pdf
31) Recovery of non compactly supported coefficients of elliptic equations on an infinite waveguide , to appear in Journal of the Institute of Mathematics of Jussieu, (2017). pdf
32) Determination of non-compactly supported electromagnetic potentials in unbounded closed waveguide, preprint, (2018). pdf
Problèmes inverses sur un guide d'ondes infini
33) Carleman estimate for infinite cylindrical quantum domains and application to inverse problems, (with Quang Sang Phan and Eric Soccorsi), Inverse Problems, 30 (2014), 055016. pdf
34) Hölder stable determination of a quantum scalar potential in unbounded cylindrical domains, (with Quang Sang Phan and Eric Soccorsi), Journal of Mathematical Analysis and Applications, 426 (2015), 194-210. pdf
35) Stability of the determination of a coefficient for wave equations in an infinite waveguide, Inverse Probl. Imaging, 8 (3) (2014), 713-732. pdf
36) An inverse stability result for non compactly supported potentials by one arbitrary lateral Neumann observation, (with Mourad Bellassoued and Eric Soccorsi), Journal of Differential Equations, 260 (2016), 7535-7562. pdf
37) An inverse problem for the magnetic Schrödinger equation in infinite cylindrical domains, (with Mourad Bellassoued and Eric Soccorsi), Publications of the Research Institute for Mathematical Sciences, 54 (2018), 679-728. pdf
Problèmes inverses de sources
38) Determination of time dependent factors of coefficients in fractional diffusion equation, (with Kenichi Fujishiro), MCRF, 6 (2016), 251-269. pdf
39) Logarithmic stability inequality in an inverse source problem for the heat equation on a waveguide, (with Diomba Sambou and Eric Soccorsi), to appear in Applicable Analysis, (2016). pdf
40) Inverse source problems in elastodynamics, (with Gang Bao, Ganghui Hu, Tao Yin), Inverse Problems, 34 (4) (2018), 045009. pdf
41) Uniqueness and stability for the recovery of a time-dependent source and initial conditions in elastodynamics, (with Ganghui Hu) preprint, (2018). pdf
42) Inverse moving source problems in electrodynamics, (with Ganghui Hu, Peijun Li, Yue Zhao) preprint, (2018). pdf
43) Reconstruction and stable recovery of source terms appearing in diffusion equations, (with Masahiro Yamamoto) preprint, (2019). pdf
Estimation de solutions d'équations des ondes
44) Global Strichartz estimates for the wave equation with a time-periodic non-trapping metric, Asymptotic Analysis, 68 (2010), 41-76. pdf
45) Cauchy problem for semilinear wave equation with time-dependent metrics, Nonlinear Analysis:Theory, Methods and Applications, 73 (2010), 2204-2212. pdf
46) Local energy decay in even dimensions for the wave equation with a time-periodic non-trapping metric and applications to Strichartz estimates, Serdica Math. J., 36 (2010), 329-370. pdf
47) Local energy decay for the wave equation with a time-periodic non-trapping metric and moving obstacle, CUBO, 3 (2012), 153-173. pdf
48) On the meromorphic continuation of the resolvent for the wave equation with time-periodic perturbations and applications, preprint (2011). pdf
Collaborateurs
Travaux soumis ou publiés:
Gang Bao, Mourad Bellassoued, Pedro Caro, Mourad Choulli, David Dos Santos Ferreira, Ali Feizmohammadi, Kenichi Fujishiro, Patricia Gaitan, Ganghui Hu, Xinchi Huang, Joonas Ilmavirta, Otared Kavian, Laurent Kayser, Yaroslav Kurylev, Matti Lassas, Peijun Li, Zhiyuan Li, Morgan Morancey, Lauri Oksanen, Quang Sang Phan, Diomba Sambou, Eric Soccorsi, Plamen Stefanov, Alexander Tetlov, Masahiro Yamamoto, Tao Yin, Yue Zhao.
Travaux en cours:
Vincent Bruneau, Peter Hislop, Xiaodong Liu, Julien Royer.
Quelques notes
Borg-Levinson theorem in dimension 1. pdf
Rellich-Kondrachov theorem for weighted space. pdf