Homepage of Youri Shestopalov
Hi my name is Youri Shestopalov
and I'm a professor in mathematics
at the
651 88
phone: +46-54-700 18 56
room: 1D368
Last modified: 2009 06 10
Short CV [*]
Research
Pedagogical merits. Research in didactics of mathematics [x]
Spectral theory of operator-valued functions [x]
Mathematical methods for electromagnetics and related items [xx]
Resume of research achievements
I perform
research in various areas of applied and numerical mathematics, mathematical
physics and mathematical modelling. In particular the
methods of the spectral theory of operator-valued functions (OFVs) [1] are
developed. Results are applied to solving various elliptic boundary value
problems of mathematical physics, e.g. for the Maxwell equations and systems of
the Helmholtz equations with piecewise constant complex-valued coefficients [2], [3]
and also in unbounded domains with mixed boundary and transmission-type
conditions and irregular multi-connected boundary and interface contours that
stretch to infinity [4],
[5].
Such problems arise also in mathematical models of multi-layer surfaces.
Results are based on the development of the theory of singular integral
operators and the spectral theory of integral OFVs
with a logarithmic singularity of the kernel [6].
Other research fields are semilinear Helmholtz and
Schrödinger equations with variable coefficients [7] and
direct and inverse scattering problems in domains with noncompact
boundaries [8]
These problems are connected with the modeling of wave propagation in layered
structures filled with nonlinear media [9],
[10].
Applied studies were also focused on numerical solution to boundary value and
transmission problems for the Helmholtz equations in unbounded domains by projectional methods; iteration techniques; and development
of numerical methods for integral equations with a logarithmic singularity of
the kernel.
The developed techniques are of universal character and have been recently
developed and applied [11] to the analysis of
the mathematical problems of elasticity and related items that enable one to model
paper layers and surfaces using specifically created mathematical models.
Report on scientific activities in
2002--2003.
Mathematical Methods for Electromagnetics:
A Small Introduction and Examples
Integral equations with logarithmic
kernels.
Analysis of slotted structures: Methods of operator
theory and integral equations.
The details and background of the method are in the book
Logarithmic
Integral Equations in Electromagnetics published by the VSP International Science Publishers
in 2000, ISBN 90-6764-322-X. See the VSP homepage www.vsppub.com
The PIERS 2000
presentations:
Uniqueness of Reconstructing the
Permittivity and Shape for Infinite Screens with Irregularities.
Examples of the student research works associated with the main field of studies
Task 1 for modeling: Waves in the Goubau Line.
Report 1 of Task 1.
Task 2 for modeling.
Report 1 of Task 2: Fields Scattered by a Rectangular Dielectric
Cylinder.
Teaching
I teach the
following PhD-courses: integral equations, partial differential equations,
numerical methods, and asymptotical methods.
The graduate courses are applied analysis, Fourier and vector analysis,
numerical methods, mathematical modeling, mathematical physics, optimization,
linear algebra.
Most of the listed courses are supported by compendiums (both in Swedish and
English) The compendiums can be found below.
Integral Equations
Integral Equations. A short course. Compendium
Tillämpad
analys. Kursplanering
Analys B2
Analys B2. Schema: vektoranalys
Analys B2. Kompendium
Lectures on Analysis B2 in English with the solved
problems.
Plan of the course Analysis B2 (in
English).
Gamla tentor
Tenta Delk
02, 2002-09-25.
Tenta 1.
Tenta 2.
Tenta 3.
Tenta 4.
Matematiska
modeller. Kompendiet.
Manual and Instruction of the Delkurs
3, MAA 308.