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Roudenko, Svetlana
Graduate Faculty
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Professor
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Mathematics and Statistics
,
College of Arts, Sciences & Education
sroudenk@fiu.edu
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Overview
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Overview
biography
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
Article
2023
Interaction 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
2023
Well-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
2022
Well-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
2022
Global 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
2022
Threshold 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
2022
Threshold solutions for the nonlinear Schrodinger equation
.
REVISTA MATEMATICA IBEROAMERICANA
. 38:1637-1708.
Full Text via DOI:
10.4171/RMI/1337
Web of Science:
000917913600010
2021
Behaviour of solutions to the 1D focusing stochastic L-2-critical and supercritical nonlinear Schrodinger equation with space-time white noise
Full Text via DOI:
10.1093/imamat/hxab040
Web of Science:
000743933700007
2021
Higher 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
2021
Numerical 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
2021
Dynamics 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
2021
Numerical 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
2021
Behavior of solutions to the 1D focusing stochastic nonlinear Schrodinger equation with spatially correlated noise
Full Text via DOI:
10.1007/s40072-021-00191-0
Web of Science:
000628724500001
2021
Littlewood-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
2020
Well-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
2020
Stable 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
2020
Global 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
2019
On 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
2019
Blow-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
2018
Blow-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
2018
Generalized 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
2015
Going 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
2015
A 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
2014
Modeling the influence of environment and intervention on cholera in Haiti
Full Text via DOI:
10.3390/math2030136
2013
Stability of Efficient Deterministic Compressed Sensing for Images with Chirps and Reed-Muller Sequences
Full Text via DOI:
10.4236/am.2013.41a029
2012
Blow-up solutions on a sphere for the 3D quintic NLS in the energy space
Full Text via DOI:
10.2140/apde.2012.5.475
2012
Special Issue on Mathematical Methods in Medical Imaging
.
JOURNAL OF SCIENTIFIC COMPUTING
. 50:493-494.
Full Text via DOI:
10.1007/s10915-012-9576-9
2012
Wavelet-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
2011
Maximizers for the Strichartz norm for small solutions of mass-critical NLS
Full Text via DOI:
10.2422/2036-2145.2011.2.08
2011
Efficient Deterministic Compressed Sensing for Images with Chirps and ReedMuller Codes
Full Text via DOI:
10.1137/100808794
2010
A Class of Solutions to the 3D Cubic Nonlinear Schrödinger Equation that Blows Up on a Circle
Full Text via DOI:
10.1093/amrx/abq016
2010
On Blow-up Solutions to the 3D Cubic Nonlinear Schrödinger Equation
Full Text via DOI:
10.1093/amrx/abm004
2010
Divergence 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
2010
Blow-up criteria for the 3D cubic nonlinear Schrödinger equation
.
NONLINEARITY
. 23:977-1030.
Full Text via DOI:
10.1088/0951-7715/23/4/011
2010
Threshold solutions for the focusing 3D cubic Schrödinger equation
.
REVISTA MATEMATICA IBEROAMERICANA
. 1-56.
Full Text via DOI:
10.4171/rmi/592
2009
Global 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
2009
Function spaces of variable smoothness and integrability
.
JOURNAL OF FUNCTIONAL ANALYSIS
. 256:1731-1768.
Full Text via DOI:
10.1016/j.jfa.2009.01.017
2008
A 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
2008
Traces and extensions of matrix‐weighted Besov spaces
.
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY
. 40:181-192.
Full Text via DOI:
10.1112/blms/bdm108
2008
Scattering 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
2007
MASS 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
2005
Estimates on level set integral operators in dimension two
.
JOURNAL OF GEOMETRIC ANALYSIS
. 15:405-423.
Full Text via DOI:
10.1007/bf02930979
2002
Matrix-weighted Besov spaces
.
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
. 355:273-314.
Full Text via DOI:
10.1090/s0002-9947-02-03096-9
Book Chapter
2019
Instability 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
2017
Traces and extensions of weighted sobolev and potential spaces
. 217-234.
Full Text via DOI:
10.1090/conm/693/13940
2010
A Universal Stein-Tomas Restriction Estimate for Measures in Three Dimensions
. 171-178.
Full Text via DOI:
10.1007/978-0-387-68361-4_12
2006
The role of transactional sex in spreading HIV in Nigeria
. 367-389.
Full Text via DOI:
10.1090/conm/410/07737
Conference
2019
Instability of solitons-revisited, I: The critical generalized KdV equation
. 65-88.
Full Text via DOI:
10.1090/conm/725/14546
Web of Science:
000473306800005
2019
Instability of solitons-revisited, II: The supercritical Zakharov-Kuznetsov equation
. 89-109.
Full Text via DOI:
10.1090/conm/725/14547
Web of Science:
000473306800006
2011
Criteria 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
2010
USING REED-MULLER SEQUENCES AS DETERMINISTIC COMPRESSED SENSING MATRICES FOR IMAGE RECONSTRUCTION
. 465-468.
Full Text via DOI:
10.1109/icassp.2010.5495714
2009
Image 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
Preprint
2022
Stability and instability of solitary waves in fractional generalized KdV equation in all dimensions
Full Text via DOI:
10.48550/arxiv.2210.09159
2022
Threshold solutions for the Hartree equation
Full Text via DOI:
10.48550/arxiv.2210.07344
2022
Well-posedness and dynamics of solutions to the generalized KdV with low power nonlinearity
2021
Higher dimensional generalization of the Benjamin-Ono equation: 2D case
2021
Interaction with an obstacle in the 2d focusing nonlinear Schrödinger equation
2020
Numerical study of soliton stability, resolution and interactions in the 3D Zakharov-Kuznetsov equation
Full Text via DOI:
10.48550/arxiv.2012.15225
2020
Well-posedness in weighted spaces for the generalized Hartree equation with $p<2$
Full Text via DOI:
10.48550/arxiv.2012.15246
2020
Threshold solutions for the nonlinear Schrödinger equation
Full Text via DOI:
10.48550/arxiv.2010.14434
2020
Threshold solutions in the focusing 3D cubic NLS equation outside a strictly convex obstacle
Full Text via DOI:
10.48550/arxiv.2010.07724
2020
Behavior of solutions to the 1D focusing stochastic nonlinear Schrödinger equation with spatially correlated noise
2020
Asymptotic stability of solitary waves of the 3D quadratic Zakharov-Kuznetsov equation
2020
Behavior of solutions to the 1D focusing stochastic $L^2$-critical and supercritical nonlinear Schrödinger equation with space-time white noise
2020
Numerical study of Zakharov-Kuznetsov equations in two dimensions
Full Text via DOI:
10.48550/arxiv.2002.07886
2019
On well-posedness and blow-up in the generalized Hartree equation
Full Text via DOI:
10.48550/arxiv.1910.01085
2019
Global well-posedness for low regularity data in the 2d modified Zakharov-Kuznetsov equation
Full Text via DOI:
10.48550/arxiv.1906.05822
2019
Global behavior of solutions to the focusing generalized Hartree equation
Full Text via DOI:
10.48550/arxiv.1904.05339
2018
Blow-up in finite or infinite time of the 2D cubic Zakharov-Kuznetsov equation
Full Text via DOI:
10.48550/arxiv.1810.05121
2017
Instability of solitons in the 2d cubic Zakharov-Kuznetsov equation
Full Text via DOI:
10.48550/arxiv.1711.05907
2017
Generalized KdV equation subject to a stochastic perturbation
Full Text via DOI:
10.48550/arxiv.1711.04413
2017
Instability of solitons - revisited, I: the critical generalized KdV equation
Full Text via DOI:
10.48550/arxiv.1711.03187
2017
Instability of solitons - revisited, II: the supercritical Zakharov-Kuznetsov equation
Full Text via DOI:
10.48550/arxiv.1711.03207
2014
Going beyond the threshold: scattering and blow-up in the focusing NLS equation
Full Text via DOI:
10.48550/arxiv.1409.4821
2013
Modeling the Influence of Environment and Intervention on Cholera in Haiti
Full Text via DOI:
10.48550/arxiv.1301.5899
2012
A solution to the focusing 3d NLS that blows up on a contracting sphere
Full Text via DOI:
10.48550/arxiv.1212.6236
2010
Blow-up solutions on a sphere for the 3d quintic NLS in the energy space
Full Text via DOI:
10.48550/arxiv.1007.1217
2010
Maximizers for the Strichartz norm for small solutions of mass-critical NLS
Full Text via DOI:
10.48550/arxiv.1007.0297
2010
A class of solutions to the 3d cubic nonlinear Schroedinger equation that blow-up on a circle
Full Text via DOI:
10.48550/arxiv.1002.2407
2009
Blow-up criteria for the 3d cubic nonlinear Schrödinger equation
Full Text via DOI:
10.48550/arxiv.0911.3955
2009
Divergence of infinite-variance nonradial solutions to the 3d NLS equation
Full Text via DOI:
10.48550/arxiv.0906.0203
2008
Threshold solutions for the focusing 3d cubic Schroedinger equation
Full Text via DOI:
10.48550/arxiv.0806.1752
2007
Function spaces of variable smoothness and integrability
Full Text via DOI:
10.48550/arxiv.0711.2354
2007
A universal Stein-Tomas restriction estimate for measures in three dimensions
Full Text via DOI:
10.48550/arxiv.0710.4586
2007
Scattering for the non-radial 3D cubic nonlinear Schroedinger equation
Full Text via DOI:
10.48550/arxiv.0710.3630
2007
A sharp condition for scattering of the radial 3d cubic nonlinear Schroedinger equation
Full Text via DOI:
10.48550/arxiv.math/0703235
2007
On blow-up solutions to the 3D cubic nonlinear Schroedinger equation
Full Text via DOI:
10.48550/arxiv.math/0703233
2006
A remark on the concentration phenomenon for the L^2-critical nonlinear Schrodinger equations
Full Text via DOI:
10.48550/arxiv.math/0610822
Review
2020
ON THE FOCUSING GENERALIZED HARTREE EQUATION
. 383-402.
Full Text via DOI:
10.5206/mase/10855
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
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