Alexander A. Kiselev

Alexander A. Kiselev
  • William T. Laprade Distinguished Professor of Mathematics
  • Professor of Mathematics

Research Areas and Keywords

Analysis

Fourier analysis, functional analysis

Biological Modeling

Chemotaxis, enhancement of biological reactions

Mathematical Physics

Spectral theory, Schrodinger operators

PDE & Dynamical Systems

Fluid mechanics, Euler equation, surface quasi-geostrophic equation, singularity formation, small scale creation, mixing efficiency

My current research interests focus on mathematical fluid mechanics and mathematical biology.
In the past, I have also worked on reaction-diffusion equations and spectral theory of Schredinger operators. 

Education & Training
  • Ph.D., California Institute of Technology 1997

Fellowships, Supported Research, & Other Grants

Regularity, Blow UP, and Mixing in Fluids awarded by NSF (2017 to 2020)

Topics in Applied PDE awarded by NSF (2014 to 2018)

Kiselev, A., et al. “Stability of singular spectral types under decaying pertubations.” Journal of Functional Analysis, vol. 198, no. 1, Feb. 2003, pp. 1–27. Scopus, doi:10.1016/S0022-1236(02)00053-8. Full Text

Christ, M., and A. Kiselev. “Absolutely continuous spectrum of Stark operators.” Arkiv for Matematik, vol. 41, no. 1, Jan. 2003, pp. 1–33. Scopus, doi:10.1007/BF02384565. Full Text

Killip, R., et al. “Dynamical upper bounds on wavepacket spreading.” American Journal of Mathematics, vol. 125, no. 5, Jan. 2003, pp. 1165–98. Scopus, doi:10.1353/ajm.2003.0031. Full Text

Gesztesy, F., et al. “Uniqueness results for matrix-valued Schrödinger, Jacobi, and Dirac-type operators.” Mathematische Nachrichten, vol. 239–240, Aug. 2002, pp. 103–45. Scopus, doi:10.1002/1522-2616(200206)239:1<103::AID-MANA103>3.0.CO;2-F. Full Text

Christ, M., and A. Kiselev. “Scattering and wave operators for one-dimensional Schrödinger operators with slowly decaying nonsmooth potentials.” Geometric and Functional Analysis, vol. 12, no. 6, Jan. 2002, pp. 1174–234. Scopus, doi:10.1007/s00039-002-1174-9. Full Text

Constantin, P., et al. “Quenching of flames by fluid advection.” Communications on Pure and Applied Mathematics, vol. 54, no. 11, Nov. 2001, pp. 1320–42. Scopus, doi:10.1002/cpa.3000. Full Text

Kiselev, A., and L. Ryzhik. “An upper bound for the bulk burning rate for systems.” Nonlinearity, vol. 14, no. 5, Sept. 2001, pp. 1297–310. Scopus, doi:10.1088/0951-7715/14/5/319. Full Text

Christ, M., and A. Kiselev. “WKB asymptotic behavior of almost all generalized eigenfunctions for one-dimensional Schrödinger operators with slowly decaying potentials.” Journal of Functional Analysis, vol. 179, no. 2, Feb. 2001, pp. 426–47. Scopus, doi:10.1006/jfan.2000.3688. Full Text

Christ, M., and A. Kiselev. “Maximal functions associated to filtrations.” Journal of Functional Analysis, vol. 179, no. 2, Feb. 2001, pp. 409–25. Scopus, doi:10.1006/jfan.2000.3687. Full Text

Kiselev, A., and L. Ryzhik. “Enhancement of the traveling front speeds in reaction-diffusion equations with advection.” Annales De L’Institut Henri Poincare (C) Analyse Non Lineaire, vol. 18, no. 3, Jan. 2001, pp. 309–58. Scopus, doi:10.1016/S0294-1449(01)00068-3. Full Text

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