Publications / preprints:
- A. Arnold, S. Geevers, I. Perugia, D. Ponomarev, "On the exponential time-decay for the one-dimensional wave equation with variable coefficients" , Communications on Pure & Applied Analysis [submitted], 2022.
- A. Arnold, S. Geevers, I. Perugia, D. Ponomarev, "An adaptive finite element method for high-frequency scattering problems with smoothly varying coefficients" , Computers and Mathematics with Applications [accepted], 2021.
- D. Ponomarev, "Asymptotic solution to convolution integral equations on large and small intervals" , Proceedings of the Royal Society A, 477:20210025, 2021.
- D. Ponomarev, "Asymptotic solutions of convolution integral equations with even positive definite kernels on a small or large interval" , Proceedings of UKBIM12, 2019.
- L. Baratchart, J. Leblond, D. Ponomarev, "Solution of a homogeneous version of Love type integral equation in different asymptotic regimes" , Integral Methods in Science and Engineering, Springer, 2019.
- L. Bourgeois, J. Dardé, D. Ponomarev, "An inverse obstacle problem for the wave equation in a finite time domain" , Inverse Problems and Imaging, 13 (2), 377-400, 2019.
- L. Baratchart, J. Leblond, E. Lima, D. Ponomarev, "Magnetization moment recovery using Kelvin transformation and Fourier analysis" , Journal of Physics: Conf. Ser., 904, 2017.
- J. Leblond, D. Ponomarev, "On some extremal problems for analytic functions with constraints on real or imaginary parts" , Advances in Complex Analysis and Operator Theory, 219-236, 2017.
- J. Leblond, D. Ponomarev, "Recovery of analytic functions with prescribed pointwise values on the disk from partial boundary data" , J. Inverse Ill-Posed Probl., 25 (2), 2017.
- L. Baratchart, J. Leblond, D. Ponomarev, "Constrained optimization in classes of analytic functions with prescribed pointwise values" , arXiv preprint, July 2014.
- D. Pelinovsky, D. Ponomarev, "Justification of a nonlinear Schrödinger model for laser beams in photopolymers" , Z. Angew. Math. Phys., 65, 405-433, 2014.
- D. Ponomarev, S. Leble, "Molecular zero-range potential method and its application to cyclic structures", arXiv preprint , January 2011.
- S. Leble, D. Ponomarev, "Dressing of zero-range potentials into realistic molecular potentials of finite range" , Task Quarterly, 14, 29-34, 2010.
- D. Ponomarev, O. Nagornov, "On effective wave propagation characteristics in porous fluid-saturated medium containing fluid inclusions" , Geophys. J. Int., 182 (2), 1043-1057, 2010.
- D. Ponomarev, "High-order time integration Leap-Frog schemes combined with a Discontinuous Galerkin method for the solution of the Maxwell equations" , INRIA preprint, October 2009.
- O. Nagornov, D. Ponomarev, "Plane wave scattering on spherical inclusions of different types in fluid-saturated porous media" [accepted with minor revisions in Mechanics of Solids; in Russian], September 2009.
Papers in preparation:
- "Revisiting the limiting amplitude principle for the wave equation with variable coefficients" (with A. Arnold, S. Geevers, I. Perugia).
- "On a transformation of Schrödinger equation to a simple first order equation with complex conjugation: theoretical and practical applications".
- "On some space-time integral equations pertinent to the punch problem with wear".
- "Recovery of magnetization features from partial field measurements: Fourier and Kelvin transforms approaches" (with J. Leblond, L. Baratchart, E. Lima).
- "On the asymptotic extension of convolution theorem for Fourier cosine transform for certain integral equations on half-line".
- "New method for construction of asymptotic solution for Prandtl lifting line equation".
- "Some inverse problems with partial data", Ph.D. Thesis , Université Nice - Sophia Antipolis / INRIA Méditerranée, France, defended on 14/06/2016, supervised by Juliette Leblond, Laurent Baratchart.
- "Justification of a nonlinear Schrödinger model for polymers", M.Sc. Thesis , McMaster University [Department of Mathematics and Statistics], Canada, defended on 03/05/2012, supervised by Dmitry Pelinovsky.
- "Electronic states in Zero-Range Potential models of nanostructures with a cyclic symmetry", M.Sc. Thesis , Gdansk University of Technology [Faculty of Theoretical Physics and Applied Mathematics], Poland, defended on 22/06/2010, supervised by Sergey Leble.