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Yavar KIAN
Professeur des universités, Laboratoire de Mathématiques Raphaël Salem (LMRS), UMR 6085
UFR des Sciences et Techniques Université de Rouen Normandie
Avenue de l'Université, BP.12 76801 Saint-Étienne-du-Rouvray, France
Google Scholar: https://scholar.google.fr/citations?user=lpk20vUAAAAJ&hl=fr
ORCID: https://orcid.org/0000-0002-5588-3600
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), Journal of Spectral Theory, 11 (2021), 1107-1143. 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
16) Recovery of non-smooth coefficients appearing in anisotropic wave equations, (with Ali Feizmohammadi), Asymptotic Analysis, 131 (2023), 513-539. 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
17) On the determination of nonlinear terms appearing in semilinear hyperbolic equations,J. London Math. Soc., 104 (2021), 572-595.. pdf
18) Partial data inverse problems for quasilinear conductivity equations, (with Katya Krupchyk, Gunther Uhlmann), Math. Ann., 385 (2023), 1611-1638. pdf
19) Recovery of nonlinear terms for reaction diffusion equations from boundary measurement, (with Gunther Uhlmann), Arch. Rational Mech. Anal., 247 (2023), https://doi.org/10.1007/s00205-022-01831-y. pdf
20) The Calderón inverse problem for isotropic quasilinear conductivities, (with Cătălin I. Cârstea, Ali Feizmohammadi, Katya Krupchyk, Gunther Uhlmann), Advances in Mathematics, 391 (2021), 107956. pdf
21) An inverse problem for a quasilinear convection--diffusion equation, (with Ali Feizmohammadi and Gunther Uhlmann), Nonlinear Analysis: Theory, Methods & Applications, 222 (2022), 112921. pdf
22) Lipschitz and Hölder stable determination of nonlinear terms for elliptic equations, Nonlinearity, 36 (2023), 1302-1322. pdf
23) On determining and breaking the gauge class in inverse problems for reaction-diffusion equations, (with T. Liimatainen, Y-H. Lin), preprint. pdf
24) Rigidity of inverse problems for nonlinear elliptic equations on manifolds, (with A. Feizmohammadi and L. Oksanen), preprint. pdf
Équations de diffusion fractionnaire en temps
25) On existence and uniqueness of solutions for semilinear fractional wave equations, (with Masahiro Yamamoto) Fractional Calculus and Applied Analysis, 20 (2017), 117-138. pdf
26) 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
27) On time-fractional diffusion equations with space-dependent variable order, (with Eric Soccorsi and Masahiro Yamamoto), Annales Henri Poincaré, 19 (2018), 3855-3881. pdf
28) Initial-boundary value problem for distributed order time-fractional diffusion equations, (with Zhiyuan Li, Eric Soccorsi), Asymptotic Analysis, 115 (2019), 95-126. pdf
29) Asymptotic estimates of solutions to time-fractional diffusion equations with space-dependent variable order, (with Diomba Sambou, Eric Soccorsi), preprint, (2019). pdf
30) The uniqueness of inverse problems for a fractionalequation with a single measurement, (with Zhiyuan Li, Yikan Liu, Masahiro Yamamoto), Math. Ann., 380 (2021), 1465-1495. pdf
31) Identification of time-varying source term in time-fractional diffusion equations, (with E. Soccorsi, Q. Xue, M. Yamamoto), Communication in Mathematical Sciences, 20 (2022), 53-84. pdf
32) Well-posedness for weak and strong solutions of non-homogeneous initial boundary value problems for fractional diffusion equations, (with M. Yamamoto), Fract. Calc. Appl. Anal., 24 (2021), 168-201. pdf
33) Simultaneous determination of different class of parameters for a diffusion equation from a single measurement, Inverse Problems, 38 (2022), 075008. pdf
34) Recovery of the Order of Derivation for Fractional Diffusion Equations in an Unknown Medium, (with B. Jin), SIAM J. Appl. Math., 82 (2022), 1045-1067. pdf
35) Reconstruction of a space-time dependent source in subdiffusion models via a perturbation approach, (with B. Jin and Z. Zhou), SIAM J. Math. Anal. , 53 (2021), 4445-4473. pdf
36) Recovering multiple fractional orders in time-fractional diffusion in an unknown medium, (with B. Jin), Proceedings of the Royal Society A, 477 (2021), 20210468. pdf
37) Uniqueness of Inverse Source Problems for General Evolution Equations, Commun. Contemp. Math., (with Yikan Liu, Masahiro Yamamoto), 25 (2023), Article ID 2250009, 33 p.. pdf
38) The enclosure method for the detection of variable order in fractional diffusion equations, (with M. Ikehata), Inverse Probl. Imaging, 17 (2023), 180-202.
39) Recovery of a distributed order fractional derivative in an unknown medium, (with B. Jin), to appear in Communication in Mathematical Sciences. pdf
40) Inverse problems for subdiffusion from observation at an unknown terminal time, (with B. Jin and Z. Zhou), to appear in SIAM J. Appl. Math.. pdf
41) Logarithmic stable recovery of the source and the initial state of time fractional diffusion equations, (with Eric Soccorci and Faouzi Triki), to appear in SIAM J. Math. Anal.. pdf
42) Equivalence of definitions of solutions for some class of fractional diffusion equations, to appear in Mathematische Nachrichten, DOI: 10.1002/mana.202100617. pdf
43) Inverse source problem with a posteriori boundary measurement for fractional diffusion equations, (with J. Janno), to appear in Mathematical Methods in the Applied Sciences, DOI: 10.1002/mma.9432. pdf
Application à l'imagerie
44) Determination of source and initial values for acoustic equations with a time-fractional attenuation, (with X. Huang, E. Soccorsi, M. Yamamoto), to appear in Analysis and Application, DOI: 10.1142/S0219530523500100. pdf
45) Determination of the sound speed and an initial source in photoacoustic tomography, (with Gunther Uhlmann), preprint. pdf
Problèmes inverses spectraux
46) 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
47) 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
48) A multidimensional Borg-Levinson theorem for magnetic Schrödinger operators with partial spectral data, Journal of Spectral Theory, 8 (2018), 235–269. pdf
49) A Borg-Levinson theorem for magnetic Schrödinger operators on a Riemannian manifold, (with M. Bellassoued, M. Choulli, D. D. Feirrera, P. Stefanov), Ann. Inst. Fourier, 71 (2021), 2471-2517. pdf
50) Identification of unbounded electric potentials through asymptotic boundary spectral data, (with M. Bellassoued,Y. Mannoubi, E. Soccorsi), preprint, arXiv:2201.05414.
Problèmes inverses utilisant la méthode du contrôle aux bords
51) Application of the boundary control method to partial data Borg-Levinson inverse spectral problem, (with Morgan Morancey and Lauri Oksanen), MCRF, 9 (2019), 289-312. pdf
52) 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
53) 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
54) 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
55) 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
56) 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
57) Determination of non-compactly supported electromagnetic potentials in unbounded closed waveguide, Revista Matemática Iberoamericana, 36 (2020), 671-710.. pdf
58) Stable recovery of non-compactly supported electromagnetic potentials in unbounded domain, (with Yosra Soussi), Mathematical Methods in the Applied Sciences, 44 (2021), 13421-13447.
Problèmes inverses sur un guide d'ondes infini
59) 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
60) 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
61) Stability of the determination of a coefficient for wave equations in an infinite waveguide, Inverse Probl. Imaging, 8 (3) (2014), 713-732. pdf
62) 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
63) 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
64) Determination of time dependent factors of coefficients in fractional diffusion equation, (with Kenichi Fujishiro), MCRF, 6 (2016), 251-269. pdf
65) 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
66) Inverse source problems in elastodynamics, (with Gang Bao, Ganghui Hu, Tao Yin), Inverse Problems, 34 (4) (2018), 045009. pdf
67) Uniqueness and stability for the recovery of a time-dependent source in elastodynamics, (with Ganghui Hu) Inverse Probl. Imaging., 14 (2020), 463-487. pdf
68) Inverse moving source problems in electrodynamics, (with Ganghui Hu, Peijun Li, Yue Zhao) Inverse Problems, 35 (2019), 075001 . pdf
69) Reconstruction and stable recovery of source terms appearing in diffusion equations, (with Masahiro Yamamoto), Inverse Problems, 35 (2019), 115006. pdf
70) 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
71) Inverse parabolic problems of determining functions with one spatial-component independence by Carleman estimate, (with O. Y. Imanuvilov and M. Yamamoto), J. Inverse Ill-Posed Probl., 30 (2022), 191-203.
Estimation de solutions d'équations des ondes
72) Global Strichartz estimates for the wave equation with a time-periodic non-trapping metric, Asymptotic Analysis, 68 (2010), 41-76. pdf
73) Cauchy problem for semilinear wave equation with time-dependent metrics, Nonlinear Analysis:Theory, Methods and Applications, 73 (2010), 2204-2212. pdf
74) 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
75) Local energy decay for the wave equation with a time-periodic non-trapping metric and moving obstacle, CUBO, 3 (2012), 153-173. pdf
76) 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, Masaru Ikehata, 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, Faouzi Triki, Gunther Uhlmann, Qi Xue, Masahiro Yamamoto, Tao Yin, Yue Zhao, Zhi Zhou.
Travaux en cours:
Vincent Bruneau, Abdellatif El Badia, Peter Hislop, Xiaodong Liu, Julien Royer.
Quelques notes
Borg-Levinson theorem in dimension 1. pdf
Rellich-Kondrachov theorem for weighted space. pdf
Lecture on Calderon problem. pdf