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Yavar KIAN


Maître de conférences, Centre de Physique Théorique (CPT), UMR-7332

Aix Marseille Université

Campus de Luminy, Case 907

13288 Marseille cedex 9, France

yavar.kian@univ-amu.fr

Tel : 04 91 26 95 29

CV: voir ici

Thèmes de recherche

Mes principaux thèmes de recherche sont:


  • Problèmes inverses pour des équations aux dérivées partielles non-linéaires (équations elliptiques, hyperboliques, paraboliques).

  • Problèmes inverses et directs (existence de solution) pour des équations de diffusion fractionnaire en temps.

  • Problèmes inverses consistant à déterminer des coefficients pour différentes équations aux dérivées partielles d'évolution (Schrödinger, hyperbolique, parabolique).

  • Problèmes inverses de sources.

  • Problème de Calderón sur un domaine non-borné.

  • Problèmes inverses spectraux.

  • Problèmes inverses sur des variétés riemanniennes (problèmes inverses pour des équations aux dérivées partielles et problèmes inverses spectraux).

  • Problèmes inverses pour différentes équations aux dérivées partielles d'évolution (Schrödinger, hyperbolique) sur un guide d'ondes.

  • Estimations (estimations dispersives et estimations de Strichartz) et étude du comportement asymptotique pour des équations aux dérivées partielles (hyperboliques et équations de diffusion fractionnaire en temps).

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), IMRN, 2019 (2019), 5087–5126. pdf

10) Hölder stably determining the time-dependent electromagnetic potential of the Schrödinger equation, (with Eric Soccorsi), SIAM J. Math. Anal., 51 (2019), 627-647. 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), to appear in Journal of spectral Theory. pdf

14) Hölder Stable Recovery of Time-Dependent Electromagnetic Potentials Appearing in a Dynamical Anisotropic Schrödinger Equation, (with Alexander Tetlow), Inverse Probl. Imaging, 14 (2020), 819-839. pdf

15) Recovery of non-smooth coefficients appearing in anisotropic wave equations, (with Ali Feizmohammadi), SIAM J. Math. Anal., 51 (2019), 4953-4976. 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, à paraître dans J. London Math. Soc., (2018). pdf

17) Partial data inverse problems for quasilinear conductivity equations, (with Katya Krupchyk, Gunther Uhlmann), preprint. pdf

18) Recovery of nonlinear terms for reaction diffusion equations from boundary measurement, (with Gunther Uhlmann), preprint. pdf

19) The Calderón inverse problem for isotropic quasilinear conductivities, (with Cătălin I. Cârstea, Ali Feizmohammadi, Katya Krupchyk, Gunther Uhlmann), preprint. pdf


Équations de diffusion fractionnaire en temps


20) On existence and uniqueness of solutions for semilinear fractional wave equations, (with Masahiro Yamamoto) Fractional Calculus and Applied Analysis, 20 (2017), 117-138. pdf

21) 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

22) On time-fractional diffusion equations with space-dependent variable order, (with Eric Soccorsi and Masahiro Yamamoto), Annales Henri Poincaré, 19 (2018), 3855-3881. pdf

23) Initial-boundary value problem for distributed order time-fractional diffusion equations, (with Zhiyuan Li, Eric Soccorsi), Asymptotic Analysis, 115 (2019), 95-126. pdf

24) Asymptotic estimates of solutions to time-fractional diffusion equations with space-dependent variable order, (with Diomba Sambou, Eric Soccorsi), preprint, (2019). pdf

25) The uniqueness of inverse problems for a fractionalequation with a single measurement, (with Zhiyuan Li, Yikan Liu, Masahiro Yamamoto), to appear in Mathematishe Annalen, (2019). pdf

26) Identification of time-varying source term in time-fractional diffusion equations, (with E. Soccorsi, Q. Xue, M. Yamamoto), prepint, (2019). pdf

27) Well-posedness for weak and strong solutions of non-homogeneous initial boundary value problems for fractional diffusion equations, (with M. Yamamoto), à paraître dans Fractional Calculus and Applied Analysis. pdf

28) Simultaneous determination of coefficients, internal sources and an obstacle of a diffusion equation from a single measurement, prepint, (2020). pdf

29) Recovery of the Order of Derivation for Fractional Diffusion Equations in an Unknown Medium, (with B. Jin), preprint, (2021). pdf

30) Reconstruction of a space-time dependent source in subdiffusion models via a perturbation approach, (with B. Jin and Z. Zhou), à paraître dans SIAM J. Math. Anal. . pdf


Problèmes inverses spectraux


31) 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

32) 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

33) A multidimensional Borg-Levinson theorem for magnetic Schrödinger operators with partial spectral data, Journal of Spectral Theory, 8 (2018), 235–269. pdf

34) A Borg-Levinson theorem for magnetic Schrödinger operators on a Riemannian manifold, (with M. Bellassoued, M. Choulli, D. D. Feirrera, P. Stefanov), à paraître dans Annales Institut Fourier, (2018). pdf


Problèmes inverses utilisant la méthode du contrôle aux bords


35) Application of the boundary control method to partial data Borg-Levinson inverse spectral problem, (with Morgan Morancey and Lauri Oksanen), (2017), MCRF, 9 (2019), 289-312. pdf

36) Unique recovery of lower order coefficients for hyperbolic equations from data on disjoint sets, (with Yaroslav Kurylev, Matti Lassas and Lauri Oksanen), Journal of Differential Equations, 267 (2019), no. 4, 2210-2238. pdf


Problème de Calderón


37) 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

38) 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

39) 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

40) Recovery of non compactly supported coefficients of elliptic equations on an infinite waveguide , Journal of the Institute of Mathematics of Jussieu, 19 (2020), 1573-1600. pdf

41) Determination of non-compactly supported electromagnetic potentials in unbounded closed waveguide, Revista Matemática Iberoamericana, 36 (2020), 671-710.. pdf


Problèmes inverses sur un guide d'ondes infini


42) 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

43) 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

44) Stability of the determination of a coefficient for wave equations in an infinite waveguide, Inverse Probl. Imaging, 8 (3) (2014), 713-732. pdf

45) 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

46) 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


47) Determination of time dependent factors of coefficients in fractional diffusion equation, (with Kenichi Fujishiro), MCRF, 6 (2016), 251-269. pdf

48) Logarithmic stability inequality in an inverse source problem for the heat equation on a waveguide, (with Diomba Sambou and Eric Soccorsi), Applicable Analysis, 99 (2020), 2210-2228.. pdf

49) Inverse source problems in elastodynamics, (with Gang Bao, Ganghui Hu, Tao Yin), Inverse Problems, 34 (4) (2018), 045009. pdf

50) Uniqueness and stability for the recovery of a time-dependent source in elastodynamics, (with Ganghui Hu) Inverse Probl. Imaging., 14 (2020), 463-487. pdf

51) Inverse moving source problems in electrodynamics, (with Ganghui Hu, Peijun Li, Yue Zhao) Inverse Problems, 35 (2019), 075001 . pdf

52) Reconstruction and stable recovery of source terms appearing in diffusion equations, (with Masahiro Yamamoto), Inverse Problems, 35 (2019), 115006. pdf

53) Uniqueness to some inverse source problems for the wave equation in unbounded domains, (with G. Hu and Y. Zaho), Acta Mathematicae Applicatae Sinica, English Series, Vol. 36, No. 1 (2020) 134-150. pdf


Estimation de solutions d'équations des ondes


54) Global Strichartz estimates for the wave equation with a time-periodic non-trapping metric, Asymptotic Analysis, 68 (2010), 41-76. pdf

55) Cauchy problem for semilinear wave equation with time-dependent metrics, Nonlinear Analysis:Theory, Methods and Applications, 73 (2010), 2204-2212. pdf

56) 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

57) Local energy decay for the wave equation with a time-periodic non-trapping metric and moving obstacle, CUBO, 3 (2012), 153-173. pdf

58) 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, Catalin Carstea, Mourad Choulli, David Dos Santos Ferreira, Ali Feizmohammadi, Kenichi Fujishiro, Patricia Gaitan, Ganghui Hu, Xinchi Huang, Joonas Ilmavirta, Oleg Yu. Imanuvilov, Bangti Jin, Otared Kavian, Laurent Kayser, Katya Krupchyk, Yaroslav Kurylev, Matti Lassas, Peijun Li, Zhiyuan Li, Yikan Liu, Morgan Morancey, Lauri Oksanen, Quang Sang Phan, Diomba Sambou, Eric Soccorsi, Plamen Stefanov, Alexander Tetlov, Gunther Uhlmann, Qi Xue, Masahiro Yamamoto, Tao Yin, Yue Zhao, Zhi Zhou.


Travaux en cours:

Vincent Bruneau, Abdellatif El Badia, Masaru Ikehata, Peter Hislop, Xiaodong Liu, Julien Royer, Faouzi Triki.



Quelques notes

Borg-Levinson theorem in dimension 1. pdf

Rellich-Kondrachov theorem for weighted space. pdf

Lecture on Calderon problem. pdf