Main research interests (MSC2020)

26 Real functions

     26-00 General reference works (handbooks, dictionaries, bibliographies, etc.);

     26-01 Instructional exposition (textbooks, tutorial papers, etc.) pertaining to real functions.

31 Potential theory

    31Axx Two-dimensional potential theory:

• • 31A10 Integral representations, integral operators, integral equations methods in two dimensions.

    31Bxx Higher-dimensional potential theory:

• • 31B10 Integral representations, integral operators, integral equations methods in higher dimensions.

34 Ordinary differential equations

    34Axx General theory for ordinary differential equations:

• • 34A05 Explicit solutions, first integrals of ordinary differential equations;

  • 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations;

  • 34A30 Linear ordinary differential equations and systems, general; 

  • 34A34 Nonlinear ordinary differential equations and systems, general.

35 Partial differential equations

    35Axx General topics in partial differential equations:

• 35A01 Existence problems for PDEs: global existence, local existence, non-existence;

• 35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness;

• 35A08 Fundamental solutions to PDEs;

• 35A09 Classical solutions to PDEs;

• 35A15 Variational methods applied to PDEs.

    35Bxx Qualitative properties of solutions to partial differential equations:  

• 35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or parameters of PDEs;

• 35B33 Critical exponents in context of PDEs;

• 35B40 Asymptotic behavior of solutions to PDEs;

• 35B44 Blow-up in context of PDEs;

• 35B45 A priori estimates in context of PDEs;

• 35B50 Maximum principles in context of PDEs;

• 35B51 Comparison principles in context of PDEs;

• 35B53 Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs;

• 35B65 Smoothness and regularity of solutions to PDEs.

    35Cxx Representations of solutions to partial differential equations:

• • 35C05 Solutions to PDEs in closed form;

  • 35C15 Integral representations of solutions to PDEs.

    35Dxx Generalized solutions to partial differential equations: 

• • 35D30 Weak solutions to PDEs;

  • 35D35 Strong solutions to PDEs.

    35Exx Partial differential equations and systems of partial differential equations with constant coefficients: 

• • 35E05 Fundamental solutions to PDEs and systems of PDEs with constant coefficients;

  • 35E15 Initial value problems for PDEs and systems of PDEs with constant coefficients;

  • 35E20 General theory of PDEs and systems of PDEs with constant coefficients.

    35Jxx Elliptic equations and elliptic systems:

• 35J05 Laplacian operator, Helmholtz equation (reduced wave equation), Poisson equation;

• 35J08 Greens functions for elliptic equations;

• 35J15 Second-order elliptic equations;

• 35J20 Variational methods for second-order elliptic equations;

• 35J25 Boundary value problems for second-order elliptic equations;

• 35J47 Second-order elliptic systems;

• 35J50 Variational methods for elliptic systems;

• 35J57 Boundary value problems for second-order elliptic systems;

• 35J60 Nonlinear elliptic equations;

• 35J62 Quasilinear elliptic equations;

• 35J65 Nonlinear boundary value problems for linear elliptic equations;

• 35J66 Nonlinear boundary value problems for nonlinear elliptic equations;

• 35J67 Boundary values of solutions to elliptic equations and elliptic systems;

• 35J86 Unilateral problems for linear elliptic equations and variational inequalities with linear elliptic operators;

• 35J87 Unilateral problems for nonlinear elliptic equations and variational inequalities with nonlinear elliptic operators;

• 35J88 Unilateral problems for elliptic systems and systems of variational inequalities with elliptic operators;

• 35J92 Quasilinear elliptic equations with p-Laplacian.

    35Kxx Parabolic equations and parabolic systems:

• 35K05 Heat equation;

• 35K08 Heat kernel;

• 35K10 Second-order parabolic equations;

• 35K15 Initial value problems for second-order parabolic equations;

• 35K20 Initial-boundary value problems for second-order parabolic equations;

• 35K40 Second-order parabolic systems;

• 35K45 Initial value problems for second-order parabolic systems;

• 35K51 Initial-boundary value problems for second-order parabolic systems;

• 35K55 Nonlinear parabolic equations;

• 35K57 Reaction-diffusion equations;

• 35K58 Semilinear parabolic equations;

• 35K59 Quasilinear parabolic equations;

• 35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations;

• 35K61 Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations;

• 35K85 Unilateral problems for linear parabolic equations and variational inequalities with linear parabolic operators;

• 35K86 Unilateral problems for nonlinear parabolic equations and variational inequalities with nonlinear parabolic operators;

• 35K87 Unilateral problems for parabolic systems and variational inequalities with parabolic operators;

• 35K90 Abstract parabolic equations;

• 35K92 Quasilinear parabolic equations with p-Laplacian.

    35Lxx Hyperbolic equations and hyperbolic systems:

• • 35L02 First-order hyperbolic equations;

  • 35L03 Initial value problems for first-order hyperbolic equations;

  • 35L04 Initial-boundary value problems for first-order hyperbolic equations;

  • 35L05 Wave equation;

  • 35L10 Second-order hyperbolic equations;

  • 35L15 Initial value problems for second-order hyperbolic equations;

  • 35L20 Initial-boundary value problems for second-order hyperbolic equations.

     35Mxx Partial differential equations of mixed-type and mixed-type systems of partial differential equations:

• •  35M10 PDEs of mixed type;

  •  35M11 Initial value problems for PDEs of mixed type;

  •  35M12 Boundary value problems for PDEs of mixed type;

  •  35M13 Initial-boundary value problems for PDEs of mixed type;

  •  35M30 Mixed-type systems of PDEs;

  •  35M31 Initial value problems for mixed-type systems of PDEs;

  •  35M32 Boundary value problems for mixed-type systems of PDEs;

  •  35M33 Initial-boundary value problems for mixed-type systems of PDEs;

  •  35M85 Unilateral problems for linear PDEs and variational inequalities with partial differential operators of mixed type;

  •  35M86 Unilateral problems for nonlinear PDEs and nonlinear variational inequalities with partial differential operators of mixed type;

  •  35M87 Unilateral problems for mixed-type systems of PDEs and systems of variational inequalities with partial differential operators of mixed type.

    35Qxx Partial differential equations of mathematical physics and other areas of application: 

• •  35Q30 Navier-Stokes equations;

  •  35Q35 PDEs in connection with fluid mechanics;

  •  35Q60 PDEs in connection with optics and electromagnetic theory;

  •  35Q61 Maxwell equations;

  •  35Q74 PDEs in connection with mechanics of deformable solids;

  •  35Q79 PDEs in connection with classical thermodynamics and heat transfer;

  •  35Q86 PDEs in connection with geophysics;

  •  35Q92 PDEs in connection with biology, chemistry and other natural sciences;

  •  35Q93 PDEs in connection with control and optimization.

    35Rxx Miscellaneous topics in partial differential equations:

• • 35R05 PDEs with low regular coefficients and/or low regular data;

  • 35R06 PDEs with measure;

  • 35R35 Free boundary problems for PDEs;

  • 35R37 Moving boundary problems for PDEs;

  • 35R45 Partial differential inequalities and systems of partial differential inequalities.

40 Sequences, series, summability

     40-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to sequences, series, summability;

     40-01 Instructional exposition (textbooks, tutorial papers, etc.) pertaining to sequences, series, summability.

42 Harmonic analysis on Euclidean spaces

    42Bxx Harmonic analysis in several variables:

• • 42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.);

  • 42B25 Maximal functions, Littlewood-Paley theory;

  • 42B30 Hp-spaces.

46 Functional analysis

    46Axx Topological linear spaces and related structures:

• 46A03 General theory of locally convex spaces;

• 46A20 Duality theory for topological vector spaces.

    46Bxx Normed linear spaces and Banach spaces; Banach lattices:

•  46B25 Classical Banach spaces in the general theory;

•  46B50 Compactness in Banach (or normed) spaces;

•  46B70 Interpolation between normed linear spaces.

    46Exx Linear function spaces and their duals:

• 46E15 Banach spaces of continuous, differentiable or analytic functions;

• 46E20 Hilbert spaces of continuous, differentiable or analytic functions;

• 46E30 Spaces of measurable functions (Lp-spaces, Orlicz spaces, Kothe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.);

• 46E35 Sobolev spaces and other spaces of smooth functions, embedding theorems, trace theorems.

47 Operator theory

    47Hxx Nonlinear operators and their properties:

• 47H04 Set-valued operators;

• 47H05 Monotone operators and generalizations; 

• 47H06 Nonlinear accretive operators, dissipative operators, etc.; 

• 47H10 Fixed-point theorems.

49 Calculus of variations and optimal control; optimization

    49Jxx Existence theories in calculus of variations and optimal control:

• 49J15 Existence theories for optimal control problems involving ordinary differential equations;

• 49J20 Existence theories for optimal control problems involving partial differential equations; 

• 49J30 Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.);

• 49J35 Existence of solutions for minimax problems;

• 49J40 Variational inequalities;

• 49J45 Methods involving semicontinuity and convergence; relaxation;

• 49J50 Fréchet and Gateaux differentiability in optimization.

    49Kxx Optimality conditions:

• • 49K40 Sensitivity, stability, well-posedness.

    49Nxx Miscellaneous topics in calculus of variations and optimal control:

• • 49N05 Linear optimal control problems;

  • 49N15 Duality theory (optimization);

  • 49N60 Regularity of solutions in optimal control.

74 Mechanics of deformable solids

    74Axx Generalities, axiomatics, foundations of continuum mechanics of solids:

• • 74A05 Kinematics of deformation;

  • 74A10 Stress;

  • 74A15 Thermodynamics in solid mechanics;

  • 74A20 Theory of constitutive functions in solid mechanics;

  • 74A55 Theories of friction (tribology).

    74Fxx Coupling of solid mechanics with other effects:

• • 74F05 Thermal effects in solid mechanics;

  • 74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.);

  • 74F15 Electromagnetic effects in solid mechanics;

  • 74F20 Mixture effects in solid mechanics;

  • 74F25 Chemical and reactive effects in solid mechanics.

    74Lxx Special subfields of solid mechanics: 

• 74L05 Geophysical solid mechanics;

• 74L10 Soil and rock mechanics;

• 74L15 Biomechanical solid mechanics.

    74Mxx Special kinds of problems in solid mechanics:

• • 74M10 Friction in solid mechanics.

    74Nxx Phase transformations in solids:

• • 74N20 Dynamics of phase boundaries in solids;

  • 74N25 Transformations involving diffusion in solids.

76 Fluid mechanics

    76Axx Foundations, constitutive equations, rheology, hydrodynamical models of non-fluid phenomena:

• 76A02 Foundations of fluid mechanics;

• 76A05 Non-Newtonian fluids;

• 76A10 Viscoelastic fluids.

    76Bxx Incompressible inviscid fluids:

• • 76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids.

    76Dxx Incompressible viscous fluids:

• 76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids;

• 76D05 Navier-Stokes equations for incompressible viscous fluids;

• 76D07 Stokes and related (Oseen, etc.) flows;

• 76D27 Other free-boundary flows; Hele-Shaw flows.

    76Exx Hydrodynamic stability:

• 76E05 Parallel shear flows in hydrodynamic stability;

• 76E06 Convection in hydrodynamic stability;

• 76E07 Rotation in hydrodynamic stability;

• 76E19 Compressibility effects in hydrodynamic stability;

• 76E30 Nonlinear effects in hydrodynamic stability. 

    76Fxx Turbulence:

• 76F10 Shear flows and turbulence; 

• 76F60 k-ε modeling in turbulence.

    76Mxx Basic methods in fluid mechanics:

• 76M30 Variational methods applied to problems in fluid mechanics.

    76Nxx Compressible fluids and gas dynamics, general:

• 76N06 Compressible Navier-Stokes equations;

• 76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics.

    76Rxx Diffusion and convection: 

• 76R05 Forced convection;

• 76R10 Free convection;

• 76R50 Diffusion.

    76Sxx Flows in porous media; filtration;

• • 76S05 Flows in porous media; filtration; seepage.

    76Uxx Rotating fluids:

• 76U05 General theory of rotating fluids.

    76Vxx Reaction effects in flows:

• 76V05 Reaction effects in flows.

    76Wxx Magnetohydrodynamics and electrohydrodynamics:

• 76W05 Magnetohydrodynamics and electrohydrodynamics.

    76Zxx Biological fluid mechanics:

• 76Z05 Physiological flows.

78 Optics, electromagnetic theory

    78-XX Optics, electromagnetic theory:

• 78-04 Software, source code, etc. for problems pertaining to optics and electromagnetic theory;

• 78-10 Mathematical modeling or simulation for problems pertaining to optics and electromagnetic theory.

78Axx General:

• 78A25 Electromagnetic theory, general;

• 78A30 Electro- and magnetostatics;

• 78A35 Motion of charged particles;

• 78A40 Waves and radiation in optics and electromagnetic theory;

• 78A45 Diffraction, scattering;

• 78A57 Electrochemistry;

• 78A60 Lasers, masers, optical bistability, nonlinear optics;

• 78A70 Biological applications of optics and electromagnetic theory.

    78Mxx Basic methods for problems in optics and electromagnetic theory:

• 78M30 Variational methods applied to problems in optics and electromagnetic theory.

80 Classical thermodynamics, heat transfer

    80-XX Classical thermodynamics, heat transfer:

• 80-04 Software, source code, etc. for problems pertaining to classical thermodynamics;

• 80-10 Mathematical modeling or simulation for problems pertaining to classical thermodynamics.

80Axx Thermodynamics and heat transfer:

• 80A05 Foundations of thermodynamics and heat transfer;

• 80A10 Classical and relativistic thermodynamics;

• 80A17 Thermodynamics of continua;

• 80A19 Diffusive and convective heat and mass transfer, heat flow;

• 80A21 Radiative heat transfer;

• 80A22 Stefan problems, phase changes, etc.;

• 80A25 Combustion;

• 80A30 Chemical kinetics in thermodynamics and heat transfer;

• 80A32 Chemically reacting flows;

• 80A50 Chemistry (general) in thermodynamics and heat transfer.

    80Mxx Basic methods in thermodynamics and heat transfer:

• 80M30 Variational methods applied to problems in thermodynamics and heat transfer.

86 Geophysics

    86Axx Geophysics:

• • 86A05 Hydrology, hydrography, oceanography;

  • 86A25 Geo-electricity and geomagnetism;

  • 86A40 Glaciology;

  • 86A60 Geological problems;

  • 86A70 Vulcanology; magma and lava flow.

92 Biology and other natural sciences

    92Cxx Physiological, cellular and medical topics:

• 92C05 Biophysics;

• 92C10 Biomechanics;

• 92C20 Neural biology;

• 92C30 Physiology (general);

• 92C35 Physiological flow;

• 92C37 Cell biology;

• 92C40 Biochemistry, molecular biology;

• 92C50 Medical applications (general).

     92Exx Chemistry:

• 92E20 Classical flows, reactions, etc. in chemistry.

97 Mathematics education

    97Gxx Geometry education:

• • 97G30 Areas and volumes (educational aspects);

  • 97G40 Plane and solid geometry (educational aspects);

  • 97G50 Transformation geometry (educational aspects);

  • 97G60 Plane and spherical trigonometry (educational aspects);

  • 97G70 Analytic geometry. Vector algebra (educational aspects);

  • 97G80 Descriptive geometry (educational aspects).

    97Hxx Algebra education:

• • 97H20 Elementary algebra (educational aspects);

  • 97H30 Equations and inequalities (educational aspects); 

  • 97H60 Linear algebra (educational aspects).

    97Ixx Analysis education:

• • 97I20 Mappings and functions (educational aspects);

  • 97I30 Sequences and series (educational aspects);

  • 97I40 Differential calculus (educational aspects);

  • 97I50 Integral calculus (educational aspects);

  • 97I60 Functions of several variables (educational aspects).

    97Mxx Education of mathematical modeling and applications of mathematics:

• 97M10 Modeling and interdisciplinarity (aspects of mathematics education);

• 97M50 Physics, astronomy, technology, engineering (aspects of mathematics education);

• 97M60 Biology, chemistry, medicine (aspects of mathematics education);

• 97M80 Arts, music, language, architecture (aspects of mathematics education).

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