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RESEARCH INTERESTS
The most part of my sienti ativity is devoted to the study of innitedimensional dissipative dynamial systems generated by partial dierential equations of mathematial physis. The area of my sienti interests an be desribed
as follows:
I) General theory:
1) dissipative dynamis in large and unbounded domains:
a) Quanitative and qualitative desription of the omplexity of spatiotemporal struture of tra jetories;
b) pattern formation, spatial omplexity and spatial haos;
) temporal evolution of spatially haoti patterns and spae-time haos
d) Kolmogorov's entropy, multi-dimensional Bernouli shemes and relations with statistis and information theory.
2) Finite-dimensional redution, invariant manifolds and estimates of the
number of eetive degrees of freedom.
3) Dynamis in spatially non-homogeneous media: homogenization and patterning.
4) Solitary waves, pulses, traveling fronts and other loalized strutures.
Weak interation in multi-pulse strutures (see the researh plan).
II) Appliations:
1) reation-diusion and reation-diusion-drift problems in large domains;
2) phase-transition: various generalizations of Cahn-Hilliard and phase-eld
models, boundary and memory eets;
3) Porous-media equations and other degenerate problems;
4) Wave equations and nonlinear optis;
5) Hydrodynamis in large and unbounded domains.
The most part of my sienti ativity is devoted to the study of innitedimensional dissipative dynamial systems generated by partial dierential equations of mathematial physis. The area of my sienti interests an be desribed
as follows:
I) General theory:
1) dissipative dynamis in large and unbounded domains:
a) Quanitative and qualitative desription of the omplexity of spatiotemporal struture of tra jetories;
b) pattern formation, spatial omplexity and spatial haos;
) temporal evolution of spatially haoti patterns and spae-time haos
d) Kolmogorov's entropy, multi-dimensional Bernouli shemes and relations with statistis and information theory.
2) Finite-dimensional redution, invariant manifolds and estimates of the
number of eetive degrees of freedom.
3) Dynamis in spatially non-homogeneous media: homogenization and patterning.
4) Solitary waves, pulses, traveling fronts and other loalized strutures.
Weak interation in multi-pulse strutures (see the researh plan).
II) Appliations:
1) reation-diusion and reation-diusion-drift problems in large domains;
2) phase-transition: various generalizations of Cahn-Hilliard and phase-eld
models, boundary and memory eets;
3) Porous-media equations and other degenerate problems;
4) Wave equations and nonlinear optis;
5) Hydrodynamis in large and unbounded domains.
Research Interests
Papers共 197 篇Author StatisticsCo-AuthorSimilar Experts
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ANALYSIS & PDEno. 2 (2024): 499-533
Doklady Mathematicspp.1-4, (2024)
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETYno. 3 (2023): 1071-1085
RUSSIAN MATHEMATICAL SURVEYSno. 4 (2023): 635-777
CoRRno. 3 (2023): 2242-2281
Известия Академии наук. Российская академия наук. Серия математическаяno. 1 (2023): 161-210
Математический сборникMatematicheskii Sbornikno. 3 (2023): 120-134
Dominic Stone,Sergey Zelik
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICSpp.1-42, (2023)
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