Complex analytic and functional analytic methods are used extensively to treat
complex ordinary and partial differential equations. The main subject of the session
will be higher order partial differential equations. Integral representations, boundary
value problems, singular integral equations, properties of integral transforms,
polyharmonic Green, Robin, Neumann functions are related.
articular subjects will be special equations as the Vekua equation,
Poisson equation, Bitsadze equation, inhomogeneous biharmonic equation.
Hyperanalytic function theory as a tool for treating elliptic systems in plane domains,
systems in several complex variables, metaanalytic function theory,
Riemann-Hilbert problem and applications e.g. for orthogonal polynomials might be also discussed.
Ordinary complex differential equations and applications in mathematical physics is another subject of the session.
The main attention will be paid to analytic-type results in complex analysis, especially those which have applications in Mathematical Physics, Mechanics, Chemistry, Biology, Medicine, Economics etc. Among the methods under consideration are: boundary value problems for holomorphic and harmonic functions and their generalisations, singular integral equations, potential analysis, conformal mappings, functional equations, entire and meromorphic functions, elliptic and doubly periodic functions etc.
Applications in Fluid Mechanics, Composite Materials, Porous Media, Hydro- Aero- and Thermo-Dynamics, Elasticity, Elasto-Plasticity, will be the most considered at the session.
Swanhild Bernstein, Uwe Kähler, Irene Sabadini, Frank Sommen
You can find the preliminary program and titles
As with the last editions we plan to have a session by the special interest group in Clifford and Quaternionic Analysis.
This session aims to present recent advances in the field or, more in general, hypercomplex analysis intended as the study of function
theories related to continuous and discrete Dirac operators and systems of partial differential operators taking values in a Clifford
algebra. Talks on theoretical advances as wells as on applications, such as numerical analysis of PDE's, operator theory, signal and
image processing, robotics, and physics, are most welcome.
The aim of this session is bring together leading experts and researchers in fixed
point theory and to assess new developments, ideas and methods in this important and
dynamic field. Additional emphasis will be put on applications in related fields,
as well as other sciences, such as the natural sciences, economics, finance, computers and engineering.
The session "Spaces of differentiable functions of several real variables and applications" intends to cover various aspects of the theory of Real Variables Function Spaces (Lebesgue, Orlich, Sobolev, Nikol'skii-Besov, Lizorkin-Triebel, Morrey, Campanato, and other spaces with zero or non-zero smoothness), such as imbedding properties, density of nice functions, weight problems, trace problems, extension theorems, duality theory etc. Various generalizations of these spaces are welcome, such as for example Orlicz-Sobolev spaces, in particular generalized Lebesgue-Sobolev spaces of variable order, Morrey-Sobolev spaces, Musielak-Orlich spaces and their Sobolev counterparts etc. Other topics: any inequalities related to these spaces, properties of operators of real analysis acting in such spaces and also various applications to partial differential equations and integral equations.
The session is devoted to theory and application of generalized functions, which comprise, among others, distributions, ultradistributions, hyperfunctions and algebras of generalized functions. Applications include, but are not restricted to, linear and nonlinear partial differential equations, asymptotic analysis, geometry, mathematical physics, stochastic processes, and harmonic analysis, both in theoretical and numerical aspects.
This year, the special session will feature a number of talks on generalized functions in harmonic analysis. However, the session is open to contributions on any aspect of generalized functions and their applications.
K. Yagdjian, F. Hirosawa (Yamaguchi), M. Reissig (Freiberg)
You can find the preliminary program, titles of talks and abstracts
The goal of the session is to discuss the state-of-the-art of qualitative properties of solutions of dispersive equations. Among other things, representations of solutions, L_p-L_q estimates, Strichartz estimates, and dispersive estimates, as well as their applications to the nonlinear evolution models are of interest. The question of the influence of low regularity coefficients on the well-posedness of the Cauchy problem is another key topic.
I. Lasiecka (Virginia), J. Webster, (Oregon), G. Avalos (Nebraska)
Within the larger context of nonlinear evolution equations, we will focus on
systems of PDEs which exhibit a hyperbolic or parabolic-hyperbolic structure in
the framework of coupled systems with an interface. The topics of this special
session will revolve around qualitative and quantitative properties of solutions to
such equations: existence and uniqueness, regularity, and long time asymptotic
behavior of solutions. These will be discussed in the cases of both bounded and
unbounded domains. Associated control theoretic questions such as stabilization,
controllability, and optimal control will be addressed as well.
Of particular interest in this session will be interactions which involve nonlinearity and/or geometric considerations. Several methods of analysis for such problems
will be presented. We anticipate the discussion of specific problems arising in applications, such as fluid-structure and flow-structure interactions, nonlinear acoustics,
traveling waves in elasticity and viscoelasticity, plasma dynamics, and semiconduc-
The Session intends to discuss various nonlinear partial differential equations in mathematical physics. Among possible arguments the following ones shall be discussed: existence and qualitative properties of the solutions, existence of wave operators and scattering for these problems, stability of solitary waves and other special solutions.
The theory of the mathematics is important, but it is also important to apply it to real life.
This session intends to discuss not only basic theoretical results on mathematics, especially
wavelet analysis or Fourier analysis, but also the applied mathematics related to the research in engineering,
medicine, acoustics, and the other various fields.
Organizers: Saburou Saitoh (Aveiro), Juri Rappoport (Moscow)
Integral transforms and reproducing kernels are the fundamental
concepts and methods; indeed, they will appear in complex analysis,
functional analysis, operator theory, PDEs, stochastic theory,
harmonic analysis, approximation theory, sampling theory, inverse
problems, learning theory, support vector method, kernel method,
discretization principle, Tikhonov regularization, integral equations,
interpolation problems, matrix theory, inequalities, orthogonal systems,
and so on. We expect to gather related mathematicians and to discuss
our research topics and their applications from various viewpoints on
the fundamental concept.
Luigi Rodino (Torino), Joachim Toft (Växjö) and M. W. Wong (Toronto)
This is a special session in the mathematics, applications and numerical analysis of pseudo-differential operators. Pseudo-differential operators are understood in a very broad sense embracing but not limited to harmonic analysis, operator theory and algebras, partial differential equations, geometry, mathematical physics and applications in engineering, geophysics and medical sciences.
Robert Gilbert (Newark), Juri Rappoport (Moscow), Vladimir Yakushev (Moscow).
Mathematical simulation of medical and biological systems on the basis
of methods of analysis, mechanics of continua and computing methods,
dynamic problems of biomechanics, mathematical methods in ophthalmology,
simulation of intraocular eye pressure measurement, virtual physiological
human analysis, computational assisted surgery, implants and transplants
analysis, medical visualization analysis, statistical analysis of medical
dates, web applications, mobile health assistance.
S. Grudsky (Mexico City), N. Vasilevski (Mexico City).
The idea of the session is to bring together the experts actively
working on Toeplitz operators acting on Bergman, Fock or Hardy spaces,
as well as in various related areas where Toeplitz operators play an
essential role, such as asymptotic linear algebra, quantisation,
approximation, singular integral and convolution type operators,
financial mathematics, etc. We expect that the results presented,
together with fruitful discussions, will serve as a snapshot of the
current stage of the area, as well as for better understanding of the
priority directions and themes of future developments.
Sergey Tikhonov (ICREA &CRM, Barcelona), Eli Liflyand (Bar-Ilan University, Israel)
Approximation Theory and Fourier Analysis are frequently considered as
two different, though related areas of analysis.
The aim of this session is to bring together researchers from both
subjects to open the common ground for the discussion on questions and
methods in these areas.
The main topics of the section include classical and modern problems
in both areas such as
Convergence problems of the Fourier series/transforms; Function
spaces; Embedding theorems; Boundedness of (singular) integral
operators; Weights; Polynomial approximation, Polynomial inequalities
and applications, Orthogonal polynomials, Measures (moduli) of
smoothness and K-functionals, and applications of these topics.
L. Berezansky (Beer-Sheva), J. Diblik (Brno), A. Zafer (Kuwait), M. Zima (Rzeszow)
Qualitative theory of differential and difference equations: initial and boundary value problems,
stability, boundedness, oscillation, asymptotic behavior, positive solutions, dynamic equations on time
scales, applications to real-life problems.
This session will focus on analytic methods in complex analytic and
algebraic geometry. Topics include: hyperbolicity, Kähler-Einstein
metrics, Kähler-Ricci flow, moduli spaces, non-standard methods, p-adic
methods, positivity, representations of fundamental groups, singularities,
K. Rudol (AGH Cracow), H.G. Stark (University of Applied Sciences, Aschaffenburg),A, Grybos (AGH Cracov), D. Onchis (NuHAG & UEMR)
The purpose of this session is to present theoretical and computation
results related to the extension of the optimal single window frames
constructions to the more complex case of multi-window frames (M-frames) constructions.
We are expecting papers dealing with demanding applications involving the
optimization of multi-waveforms. Also challenges in high-D frames
constructions should be of main interest.
The purpose of this session is to present contributions to the community of mathematicians, how the queuing theory, which is present in telecommunicatoin since the figures of Erlang and Molina, will be used to model, evaluate and design computer networks, the Internet in particular. Examplary topics are: models of traffic and congestion control mechnisms, quality of service issues, the use of Markov chains, diffussion approximation and fluid flow approximation. We may also discuss software implementations and numerical problems encountered in modelling large network topologies.
The discussion group on applied mathematics includes presentations of the computer and industrial enterprises related to application of various computer and mathematical models. The main goal of these representations is to introduce into problems arising in applications; to try to create mathematical and computer methods of its solutions; to pay attention of mathematicians to applied problems.
Possible topics include:
fracture and porous media,
The session on applied mathematics is a part of the discussion group where mathematical results will be presented. The discussion group is rather discussions devoted to eventual cooperation.