PD Dr. Pavel Gurevich

gurevich_pavel
Image Credit: Pavel Gurevich

Department of Mathematics and Computer Science, Institute of Mathematics

Group Hysteresis Dynamics

Group Mathematics of Machine Learning

Principle Investigator

Address
Arnimallee 3, rear building
Room 126
14195 Berlin
Email
gurevich[at]math.fu-berlin.de

Curriculum vitae (pdf)

Research interests

  • Partial and functional differential equations
  • Hysteresis
  • Dynamical systems
  • Machine learning
  • Applications to biology
  • Applications to medicine

Current Projects

Recent Projects

Dissertations Textbook Co-editor Monograph Book chapter Journals

Dissertations:

Ph.D. thesis: 
Gurevich P. 
Solvability and asymptotics of solutions for nonlocal elliptic boundary value problems. 
2002. 
(in Russian: thesisabstract ).
Habilitation thesis: 
Gurevich P. 
Elliptic problems with nonlocal boundary conditions and Feller semigroups. 2008. 
(in Russian: thesisabstract; in English: thesis).

Textbook:

Gurevich P. Skubachevskii A. 
Application of nonlinear analysis methods to nonlocal problems of heat distribution.  
Moscow. Peoples' Friendship University of Russia. 2008 [in Russian] 
(pdf)
.

Co-editor:

O. Klein, M. Dimian, P. Gurevich, D. Knees, D. Rachinskii, S. Tikhomirov 
MURPHYS-HSFS-2014: 7th International Workshop on MUlti-Rate Processes & HYSteresis (MURPHYS) & the 2nd International Workshop on Hysteresis and Slow-Fast Systems (HSFS). 2016. J. Phys.: Conf. Ser. 727.  

(open access)
P. Gurevich, A. Korobeinikov, D. Rachinskii, V. Sobolev 
8th Workshop on Multi-Rate Processes and Hysteresis and the HSFS Workshop (Hysteresis and Slow-Fast Systems). 2017. J. Phys.: Conf. Ser. 811. 
(open access)

P. Gurevich, J. Hell, B. Sandstede, A. Scheel 
Patterns of Dynamics: International Conference on Patterns of Dynamics 
Springer Proceedings in Mathematics & Statistics. 2017
(link) 

Monograph:

Gurevich P. 
Elliptic problems with nonlocal boundary conditions and Feller semigroups.
 
Contemporary Mathematics. Fundamental Directions. V. 38 (2010). P. 3-173. 
(pdf)

Book chapter:

Curran M., Gurevich P., Tikhomirov S. 
Recent advances in reaction-diffusion equations with non-ideal relays.
In: "Control of Self-Organizing Nonlinear Systems", edited by E. Schöll, S. H. L. Klapp, P. Hövel (Springer, Berlin, Heidelberg, 2016). p. 211-234. 
(pdf)

Journals:

Gurevich P., Stuke H.
Robustness Against Outliers For Deep Neural Networks By Gradient Conjugate Priors
Preprint:  arXiv:1905.08464 [stat.ML]
(pdf)
Gurevich P.
Asymptotics of the heat kernels on 2D lattices.
Asymptotic Analysis 112 (2019) 107-124.
(pdf)
Gurevich P., Stuke H. 
Gradient conjugate priors and deep neural networks.
J. Artificial Intelligence 10.1016/j.artint.2019.103184
(pdf)
Gurevich P., Stuke H.
Pairing an arbitrary regressor with an artificial neural network estimating aleatoric uncertainty.

Neurocomputing. 10.1016/j.neucom.2019.03.031
(pdf)
Gurevich P., Ron E.
Stability of Periodic Solutions for Hysteresis-Delay Differential Equations
Journal of Dynamics and Differential Equations, 31(4), (2019) pp. 1873-1920
https://doi.org/10.1007/s10884-018-9664-0 
(pdf)
Gurevich P., Reichelt S. 
Pulses in FitzHugh Nagumo systems with rapidly oscillating coefficients
Multiscale Model. Simul. 16(2), (2018), pp. 833–856 
(pdf) 
Gurevich P., Tikhomirov S. 
Spatially discrete reaction-diffusion equations with discontinuous hysteresis. 
Ann. Inst. H. Poincaré Anal. Non Linéaire Vol. 35, No. 4, (2018), pp. 1041-1077,  https://doi.org/10.1016/j.anihpc.2017.09.006 
(pdf)
Gurevich P., Tikhomirov S. 
Rattling in spatially discrete diffusion equations with hysteresis. 
Multiscale Model. Simul. 15(3) (2017), pp. 1176-1197 
(pdf)
Gurevich P., Tikhomirov S.
Error estimates for Riemann sums of some singular functions
arXiv:1703.03203 (2017)
(pdf) 
Gurevich P., Stuke H., Kastrup A., Stuke H. and Hildebrandt H. 
Neuropsychological testing and machine learning distinguish Alzheimer's disease from other causes for cognitive impairment.
 
Front. Aging Neurosci. 9:114 (2017) 
(pdf)
Arnold M., Begun N., Gurevich P., Kwame E., Lamba H., Rachinskii D. 
Dynamics of discrete time systems with a hysteresis stop operator. 

SIAM Journal on Applied Dynamical Systems. Vol. 16, No. 1, pp. 91-119 (2017) 
(pdf)
Gurevich P. 
Asymptotics of parabolic Green's functions on lattices. 

Algebra i Analiz. 28, No. 5, pp. 21-60 (2016), English transl.: St. Petersburg Math. J. 28, pp. 569-596 (2017). 
(pdf)
Gurevich P., Vaeth M.
Stability for semilinear parabolic problems in L_2 and W^{1,2}, and interpolation spaces. 

Z. Anal. Anwendungen. 35, No. 3 (2016), 333-357. 
(Extended version: pdf)
Gurevich P., Rachinskii D. 
Asymptotics of sign-changing patterns in hysteretic systems with diffusive thresholds. 

Asymptotic Analysis. Vol. 96, pp. 1-22 (2016)
(pdf)
Friedman G., Gurevich P., McCarthy S., Rachinskii D. 
Switching behaviour of two-phenotype bacteria in varying environment. 
J. Physics: Conference Series. Vol. 585, 012012 (2015). 
(pdf)
Gurevich P., Stark H., Zeitz M. 
Feedback control of flow vorticity at low Reynolds numbers. 
The European Physical Journal E (EPJE). Vol. 38:22 (2015).
(pdf)
Gurevich P., Rachinskii D. 
Pattern formation in parabolic equations containing hysteresis with diffusive thresholds. 
J. Math. Anal. Applications. Vol. 424 No. 2, pp. 1103-1124 (2015) 
(pdf)
Gurevich P., Tikhomirov S. 
Systems of reaction-diffusion equations with spatially distributed hysteresis. 

in Proceedings of Equadiff 2013, (Mathematica Bohemica 2014). Vol. 139, No. 2 (2014), 239-257. 
(pdf)
Gurevich P., Rachinskii D. 
Well-posedness of parabolic equations containing hysteresis with diffusive thresholds. 
in Proceedings of the Steklov Institute of Mathematics. Vol. 283 (2013). P. 87-109 
(pdf)
Gurevich P., Shamin R., Tikhomirov S. 
Reaction-diffusion equations with spatially distributed hysteresis. 

SIAM J. Math. Anal. Vol. 45, No. 3, pp. 1328-1355 (2013) 
(pdf)
Gurevich P., Tikhomirov S. 
Uniqueness of transverse solutions for reaction-diffusion equations with spatially distributed hysteresis. 
Nonlinear Analysis. Vol. 75 (2012). P. 6610-6619. 
(pdf)
Gurevich P., Tikhomirov S. 
Symmetric periodic solutions of parabolic problems with discontinuous hysteresis. 

Journal of Dynamics and Differential Equations. Vol. 23. No. 4. (2011). P. 923-960. 
(pdf)
Gurevich P. 
Periodic solutions of parabolic problems with hysteresis on the boundary. 

Discrete Cont. Dynam. Systems. Series A. Volume 29, Number 3 (2011) P. 1041-1083. 
(pdf)
Gurevich P., Jaeger W. 
Parabolic problems with the Preisach hysteresis operator in boundary conditions. 

Journal of Differential Equations. Vol. 47 (2009). P. 2966-3010. 
(pdf)
Gurevich P., Jaeger W., Skubachevskii A. 
On periodicity of solutions for thermocontrol problems with hysteresis-type switches. 

SIAM J. Math. Anal. 41, No. 2 (2009). P. 733-752. 
(pdf)
Gurevich P. 
Smoothness of generalized solutions for higher-order elliptic equations with nonlocal boundary conditions. 

J. Differential Equations. 245 (2008). P. 1323-1355. 
(pdf)
Gurevich P. 
On nonexistence of Feller semigroups in the nontransversal case. 
Uspekhi Mat. Nauk. 63 , No. 3 (2008). P. 159-160. English transl. in Russian Math. Surveys. 63, No. 3 (2008). P. 565-566. 
(pdf)
Gurevich P. 
Bounded perturbations of two-dimensional diffusion processes with nonlocal conditions near the boundary. 

Mat. Zametki. 83 , No. 2 (2008) P. 181-198. English transl. in Math. Notes. 83 , No.  2 (2008). P. 162-179. 
(pdf)
Gurevich P., Jaeger W., Skubachevskii A. 
On the existence of periodic solutions to some nonlinear thermal control problems. 

Dokl. Akad. Nauk . 418, No. 2 (2008). P. 151-154. English transl. in Russian Acad. Sci. Dokl. Math. 77 , No. 1 (2008). P. 27-30. 
(pdf)
Gurevich P. 
On the existence of a Feller semigroup with atomic measure in nonlocal boundary condition. 

Trudy Mat. Inst. im. V.A. Steklova . 260 (2008). P. 164-179. English transl. in Proceedings of the Steklov Institute of Mathematics 260 (2008). P. 157-171. 
(pdf)
Gurevich P. 
Unbounded Perturbations of Two-Dimensional Diffusion Processes with Nonlocal Boundary Conditions. 

Dokl. Akad. Nauk . 417 , No. 4 (2007). English transl. in Russian Acad. Sci. Dokl. Math. 76, No. 3 (2007). P. 891-895. 
(pdf)
Gurevich P. 
On the index instability for some nonlocal elliptic problems. 

Trudy seminara imeni I.G. Petrovskogo. 26 (2007). P. 178-193. English transl. in J. Math. Sci. 143, No 4 (2007). P. 3293-3302. 
(pdf)
Gurevich P., Skubachevskii A. 
On the Fredholm and Unique Solvability of Nonlocal Elliptic Problems in Multidimensional Domains. 
Trudy MMO. 68 (2007), 288-373. English transl. in Trans. Moscow Math. Soc. 68 (2007). P. 261-336. 
(pdf)
Gurevich P. 
On the stability of the index of unbounded nonlocal operators in Sobolev spaces. 

Trudy Mat. Inst. im. V.A. Steklova. 255 (2006), 116-135. English transl. in Proceedings of the Steklov Institute of Mathematics 255 (2006). 
(pdf)
Gurevich P. 
The consistency conditions and the smoothness of generalized solutions of nonlocal elliptic problems. 

Advances in Differential Equations. 11, No. 3 (2006), 305-360. 
(pdf)
Gurevich P. 
Generalized Solutions of Nonlocal Elliptic Problems. 

Mat. Zametki. 77, No 5 (2005), 665-682; English transl. in Math. Notes 77, No 5-6 (2005), 614-629. 
(pdf)
Gurevich P. 
Smoothness of Generalized Solutions to Nonlocal Elliptic Problems on the Plane. 

Dokl. Akad. Nauk. 398, No 3 (2004), 295-299; English transl. in Russian Acad. Sci. Dokl. Math. 70 (2004), 714-718. 
(pdf)
Gurevich P. 
Solvabiblity of Nonlocal Elliptic Problems in Sobolev Spaces, II. 

Russ. J. Math. Phys. 11, No. 1 (2004), 1-44. 
(pdf)
Gurevich P. 
Solvabiblity of Nonlocal Elliptic Problems in Sobolev Spaces, I. 

Russ. J. Math. Phys. 10, No. 4 (2003), 436-466. 
(pdf)
Gurevich P. 
Non-local elliptic problems with non-linear argument transformations near the points of conjugation. 

Izv. Ross. Akad. Nauk. Ser. Mat. 67, No 6 (2003). P. 71-110. English transl. in Izv. Math. 67, No 6 (2003), 1149-1186. 
(pdf)
Gurevich P. 
Asymptotics of solutions for nonlocal elliptic problems in plane bounded domains. 
Functional Differential Equations. 10, No 1-2 (2003), P. 175-214. 
(pdf)
Gurevich P. 
Asymptotics of Solutions for Nonlocal Elliptic Problems in Plane Angles. 

Trudy seminara imeni I.G. Petrovskogo. 23 (2003); Engilsh transl. in J. Math. Sci., 120, No 3 (2004), 1295-1312. 
(pdf)
Gurevich P. 
Solvability of nonlocal elliptic problems in dihedral angles. 
Mat. Zametki. 72 (2002), 178-197; English transl. in Math. Notes 72, No 2 (2002), 158-176. 
(pdf)
Gurevich P. 
Nonlocal problems for elliptic equations in dihedral angles and the Green formula. 

Mitteilungen aus dem Mathem. Seminar Giessen, Math. Inst. Univ. Giessen, Germany, 247 (2001), 1-74. 
(pdf)
Gurevich P. 
Nonlocal elliptic problems in dihedral angles and the Green formula. 

Dokl. Akad. Nauk. 379 (2001), 735-738; English transl. in Russian Acad. Sci. Dokl. Math 64, No 1 (2001), 117-120. 
(pdf)
Gurevich P. 
Solvability of the boundary value problem for some differential-difference equations. 

Functional Differential Equations. 5 (1998), 139-157. 
(pdf)