Overview
biography
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Svetlana Roudenko is a Professor in Mathematics and Statistics and the Graduate Program Director.
Ph.D. in Mathematics, 2002, Michigan State University
M.S. in Applied Math, 1996, Obninsk State Technical University (Russia)
research interests
- Nonlinear Partial Differential Equations, Fourier Analysis, Signal and Image Analysis, Medical Imaging , Mathematical Biology
Scholarly & Creative Works
selected scholarly works & creative activities
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Article
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2023Interaction with an obstacle in the 2D focusing nonlinear Schrödinger equation. ADVANCES IN COMPUTATIONAL MATHEMATICS. 49.Full Text via DOI: 10.1007/s10444-023-10055-x
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2023Well-posedness and dynamics of solutions to the generalized KdV with low power nonlinearity. NONLINEARITY. 36:584-635.Full Text via DOI: 10.1088/1361-6544/ac93e1 Web of Science: 000907481500001
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2022Well-posedness in weighted spaces for the generalized Hartree equation with p < 2. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. 24.Full Text via DOI: 10.1142/S0219199721500747 Web of Science: 000875481200008
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2022Global Behavior of Solutions to the Focusing Generalized Hartree Equation. MICHIGAN MATHEMATICAL JOURNAL. 71:619-672.Full Text via DOI: 10.1307/mmj/20205855 Web of Science: 000842055300008
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2022Threshold solutions in the focusing 3D cubic NLS equation outside a strictly convex obstacle. JOURNAL OF FUNCTIONAL ANALYSIS. 282.Full Text via DOI: 10.1016/j.jfa.2021.109326 Web of Science: 000781808900012
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2022Threshold solutions for the nonlinear Schrodinger equation. REVISTA MATEMATICA IBEROAMERICANA. 38:1637-1708.Full Text via DOI: 10.4171/RMI/1337 Web of Science: 000917913600010
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2021Higher dimensional generalization of the Benjamin-Ono equation: 2D case. STUDIES IN APPLIED MATHEMATICS. 148:498-542.Full Text via DOI: 10.1111/sapm.12448 Web of Science: 000698199800001
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2021Numerical study of soliton stability, resolution and interactions in the 3D Zakharov-Kuznetsov equation. PHYSICA D. 423.Full Text via DOI: 10.1016/j.physd.2021.132913 Web of Science: 000661734700004
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2021Dynamics of solutions in the generalized Benjamin-Ono equation: A numerical study. JOURNAL OF COMPUTATIONAL PHYSICS. 445.Full Text via DOI: 10.1016/j.jcp.2021.110570 Web of Science: 000722631000014
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2021Numerical Study of Zakharov-Kuznetsov Equations in Two Dimensions. JOURNAL OF NONLINEAR SCIENCE. 31.Full Text via DOI: 10.1007/s00332-021-09680-x Web of Science: 000618213000001
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2021Behavior of solutions to the 1D focusing stochastic nonlinear Schrodinger equation with spatially correlated noiseFull Text via DOI: 10.1007/s40072-021-00191-0 Web of Science: 000628724500001
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2021Littlewood-Paley theory for matrix-weighted function spaces. MATHEMATISCHE ANNALEN. 380:487-537.Full Text via DOI: 10.1007/s00208-020-02088-0 Web of Science: 000608081200001
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2020Well-posedness and blow-up properties for the generalized Hartree equation. JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS. 17:727-763.Full Text via DOI: 10.1142/S0219891620500228 Web of Science: 000614111500004
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2020Stable blow-up dynamics in the L-2-critical and L-2-supercritical generalized Hartree equation. STUDIES IN APPLIED MATHEMATICS. 145:647-695.Full Text via DOI: 10.1111/sapm.12328 Web of Science: 000556598300001
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2020Global well-posedness for low regularity data in the 2d modified Zakharov-Kuznetsov equation. JOURNAL OF DIFFERENTIAL EQUATIONS. 268:7962-7997.Full Text via DOI: 10.1016/j.jde.2019.11.092 Web of Science: 000520930900024
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2019On instability of solitons in the 2d cubic Zakharov-Kuznetsov equation. SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES. 13:435-446.Full Text via DOI: 10.1007/s40863-019-00142-7 Web of Science: 000514164000006
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2019Blow-up dynamics in the mass super-critical NLS equations. PHYSICA D. 396:47-69.Full Text via DOI: 10.1016/j.physd.2019.02.015 Web of Science: 000470949700005
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2018Blow-up dynamics and spectral property in the L-2-critical nonlinear Schrodinger equation in high dimensions. NONLINEARITY. 31:4354-4392.Full Text via DOI: 10.1088/1361-6544/aacc41 Web of Science: 000441191000001
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2018Generalized KDV equation subject to a stochastic perturbation. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B. 23:1177-1198.Full Text via DOI: 10.3934/dcdsb.2018147
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2015Going Beyond the Threshold: Scattering and Blow-up in the Focusing NLS Equation. COMMUNICATIONS IN MATHEMATICAL PHYSICS. 334:1573-1615.Full Text via DOI: 10.1007/s00220-014-2202-y
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2015A Solution to the focusing 3D NLS that blows up on a contracting sphere. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. 367:3847-3872.Full Text via DOI: 10.1090/S0002-9947-2015-06057-7
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2014Modeling the influence of environment and intervention on cholera in HaitiFull Text via DOI: 10.3390/math2030136
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2012Blow-up solutions on a sphere for the 3D quintic NLS in the energy spaceFull Text via DOI: 10.2140/apde.2012.5.475
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2012Special Issue on Mathematical Methods in Medical Imaging. JOURNAL OF SCIENTIFIC COMPUTING. 50:493-494.Full Text via DOI: 10.1007/s10915-012-9576-9
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2012Wavelet-Based De-noising of Positron Emission Tomography Scans. JOURNAL OF SCIENTIFIC COMPUTING. 50:665-677.Full Text via DOI: 10.1007/s10915-011-9529-8
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2010On Blow-up Solutions to the 3D Cubic Nonlinear Schrödinger EquationFull Text via DOI: 10.1093/amrx/abm004
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2010Divergence of Infinite-Variance Nonradial Solutions to the 3D NLS Equation. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS. 35:878-905.Full Text via DOI: 10.1080/03605301003646713
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2010Blow-up criteria for the 3D cubic nonlinear Schrödinger equation. NONLINEARITY. 23:977-1030.Full Text via DOI: 10.1088/0951-7715/23/4/011
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2010Threshold solutions for the focusing 3D cubic Schrödinger equation. REVISTA MATEMATICA IBEROAMERICANA. 1-56.Full Text via DOI: 10.4171/rmi/592
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2009Global Behavior of Solutions to the Focusing 3d Cubic Nonlinear Schrödinger Equation. 11TH CONFERENCE ON THE INTERSECTIONS OF PARTICLE AND NUCLEAR PHYSICS (CIPANP 2012). 1168:1244-1247.Full Text via DOI: 10.1063/1.3241299
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2009Function spaces of variable smoothness and integrability. JOURNAL OF FUNCTIONAL ANALYSIS. 256:1731-1768.Full Text via DOI: 10.1016/j.jfa.2009.01.017
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2008A Sharp Condition for Scattering of the Radial 3D Cubic Nonlinear Schrödinger Equation. COMMUNICATIONS IN MATHEMATICAL PHYSICS. 282:435-467.Full Text via DOI: 10.1007/s00220-008-0529-y
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2008Traces and extensions of matrix‐weighted Besov spaces. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY. 40:181-192.Full Text via DOI: 10.1112/blms/bdm108
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2008Scattering for the non-radial 3D cubic nonlinear Schrödinger equation. MATHEMATICAL RESEARCH LETTERS. 15:1233-1250.Full Text via DOI: 10.4310/mrl.2008.v15.n6.a13
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2007MASS CONCENTRATION WINDOW SIZE AND STRICHARTZ NORM DIVERGENCE RATE FOR THE L2-CRITICAL NONLINEAR SHRÖDINGER EQUATION. JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS. 4:613-627.Full Text via DOI: 10.1142/s0219891607001288
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2005Estimates on level set integral operators in dimension two. JOURNAL OF GEOMETRIC ANALYSIS. 15:405-423.Full Text via DOI: 10.1007/bf02930979
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2002Matrix-weighted Besov spaces. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. 355:273-314.Full Text via DOI: 10.1090/s0002-9947-02-03096-9
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Book Chapter
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2019Instability of Solitons in the 2d Cubic Zakharov-Kuznetsov Equation. 295-371.Full Text via DOI: 10.1007/978-1-4939-9806-7_6 Web of Science: 000629743900007
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2017Traces and extensions of weighted sobolev and potential spaces. 217-234.Full Text via DOI: 10.1090/conm/693/13940
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2010A Universal Stein-Tomas Restriction Estimate for Measures in Three Dimensions. 171-178.Full Text via DOI: 10.1007/978-0-387-68361-4_12
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2006The role of transactional sex in spreading HIV in Nigeria. 367-389.Full Text via DOI: 10.1090/conm/410/07737
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Conference
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2019Instability of solitons-revisited, I: The critical generalized KdV equation. 65-88.Full Text via DOI: 10.1090/conm/725/14546 Web of Science: 000473306800005
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2019Instability of solitons-revisited, II: The supercritical Zakharov-Kuznetsov equation. 89-109.Full Text via DOI: 10.1090/conm/725/14547 Web of Science: 000473306800006
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2011Criteria for Collapse in the Focusing Nonlinear Schrödinger Equation. 11TH CONFERENCE ON THE INTERSECTIONS OF PARTICLE AND NUCLEAR PHYSICS (CIPANP 2012). 717-720.Full Text via DOI: 10.1063/1.3636831
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2010USING REED-MULLER SEQUENCES AS DETERMINISTIC COMPRESSED SENSING MATRICES FOR IMAGE RECONSTRUCTION. 465-468.Full Text via DOI: 10.1109/icassp.2010.5495714
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2009Image reconstruction by deterministic compressed sensing with chirp matrices. ADVANCED BIOMEDICAL AND CLINICAL DIAGNOSTIC SYSTEMS VII. 74971s-74971s-8.Full Text via DOI: 10.1117/12.832649
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Preprint
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2020Threshold solutions for the nonlinear Schrödinger equationFull Text via DOI: 10.48550/arxiv.2010.14434
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2020Numerical study of Zakharov-Kuznetsov equations in two dimensionsFull Text via DOI: 10.48550/arxiv.2002.07886
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2019On well-posedness and blow-up in the generalized Hartree equationFull Text via DOI: 10.48550/arxiv.1910.01085
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2019Global behavior of solutions to the focusing generalized Hartree equationFull Text via DOI: 10.48550/arxiv.1904.05339
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2017Instability of solitons in the 2d cubic Zakharov-Kuznetsov equationFull Text via DOI: 10.48550/arxiv.1711.05907
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2017Generalized KdV equation subject to a stochastic perturbationFull Text via DOI: 10.48550/arxiv.1711.04413
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2013Modeling the Influence of Environment and Intervention on Cholera in HaitiFull Text via DOI: 10.48550/arxiv.1301.5899
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2012A solution to the focusing 3d NLS that blows up on a contracting sphereFull Text via DOI: 10.48550/arxiv.1212.6236
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2010Blow-up solutions on a sphere for the 3d quintic NLS in the energy spaceFull Text via DOI: 10.48550/arxiv.1007.1217
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2010Maximizers for the Strichartz norm for small solutions of mass-critical NLSFull Text via DOI: 10.48550/arxiv.1007.0297
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2009Blow-up criteria for the 3d cubic nonlinear Schrödinger equationFull Text via DOI: 10.48550/arxiv.0911.3955
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2009Divergence of infinite-variance nonradial solutions to the 3d NLS equationFull Text via DOI: 10.48550/arxiv.0906.0203
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2008Threshold solutions for the focusing 3d cubic Schroedinger equationFull Text via DOI: 10.48550/arxiv.0806.1752
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2007Function spaces of variable smoothness and integrabilityFull Text via DOI: 10.48550/arxiv.0711.2354
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2007Scattering for the non-radial 3D cubic nonlinear Schroedinger equationFull Text via DOI: 10.48550/arxiv.0710.3630
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2007On blow-up solutions to the 3D cubic nonlinear Schroedinger equationFull Text via DOI: 10.48550/arxiv.math/0703233
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Review
Research
principal investigator on
- S-STEM: JAMS @ FIU (Joint Applied Math and Stats scholarships at FIU) awarded by National Science Foundation 2023 - 2028
- Collaborative Research: Nonlinear dynamics and spectral analysis in dispersive PDE awarded by National Science Foundation 2021 - 2024
- REU Site "AMRPU @ FIU" awarded by National Security Agency 2022 - 2024
- REU Site: Applied Mathematics Research Program for Undergraduates at FIU (AMRPU @ FIU) awarded by National Science Foundation 2021 - 2024
- Conference "V Workshop on Nonlinear Dispersive Equations" awarded by National Science Foundation 2022 - 2023
- Nonlinear phenomena in stochastic and deterministic dispersive PDE awarded by National Science Foundation 2019 - 2022
- Nonlinear Differential Equations and many particle systems awarded by National Science Foundation 2018 - 2020
- CAREER: Nonlinear phenomena in dispersive PDE awarded by National Science Foundation 2019 - 2020
Contact
full name
- Svetlana Roudenko
Identifiers
ORCID iD
- https://orcid.org/0000-0002-7407-7639 (confirmed)
