ICDDEA 2019‎ > ‎

e. Special Sessions

Variational, Topological and Set-Valued Methods for nonlinear
boundary value problems

Pasquale Candito
Mediterranean University of Reggio Calabria, Italy

Roberto Livrea
University of Palermo, Italy

Luís Sanchez
Faculdade de Ciências, ULisboa, Portugal

The aim of the session is to make a focus on some recent trends on nonlinear problems of different type, e.g., ordinary, partial differential equations and inclusions, as well as difference equations. It will be emphasized how the various methods and techniques -- of variational, topological or set-valued nature -- can be employed, separately or in combination, for studying the existence, the multiplicity and some qualitative properties of the solutions. Topics involving equations driven by nonlinear differential operators, or with the presence of singular terms, are welcome.

Boundary Value Problems for Differential and Difference Equations and Inclusions

John R. Graef
University of Tennessee at Chattanooga, USA

Feliz Minhós
University of Évora, Portugal

This session is devoted to boundary value problems for differential and difference equations and inclusions and their applications. This includes fractional, stochastic, and hybrid problems.
The techniques used may be of a variational or topological nature.

Differential Equations for Markov Chains and Models

Alexander Zeifman
Vologda State University, Russia

In this session the methods of investigation of the forward Kolmogorov system (finite or countable) and the corresponding bounds for inhomogeneous continuous-time Markov chains will be discussed, also some aspects of applications of random processes for solving boundary value problems will be studied.

Special Session on Time Scales

Martin Bohner
Missouri University of Science and Technology, USA

Stefan Hilger
Katholische Universität Eichstätt-Ingolstadt, Germany

This Special Session will present recent results in Calculus on Time Scales and Dynamic Equations. 
Contributions from related areas, such as q-difference equations, fractional difference equations are welcome.

Non-Linear Difference Equations 

Garyfalos Papaschinopoulos
Democritus University of Thrace, Greece 

Christos J. Schinas
Democritus University of Thrace

This session deals with non-linear difference equations and systems of non-linear difference equations i.e. difference equations with exponential terms, rational difference equations, etc...
Non-linear difference equations have numerous potential applications in Biology. The existence and uniqueness of equilibria, the attractivity and the global asymptotic stability of the equilibria will be studied. Centre manifold theory and other techniques can be used for this goal.

Recent advances in finite difference methods for multiphysics IBVPs

José A. Ferreira 
CMUC, University of Coimbra, Portugal

Luís Pinto
CMUC, University of Coimbra, Portugal

This special session aims to discuss recent developments in the numerical analysis of finite difference methods for multiphysics initial boundary value problems. 
Particular attention will be given to applications in Medicine and Biology.

Mathematical modelling and simulations of cardiovascular diseases

Adelia Sequeira 
Instituto Superior Técnico, Portugal

Jorge Tiago
Instituto Superior Técnico, Portugal

Cardiovascular diseases still remain the leading cause of death in developed countries. A deeper understanding of the physiopathologies associated to diseases like atherosclerosis, thrombosis or aneurysm growth and its eventual rupture has a significant impact in terms of social well-being and reduction of healthcare costs.
Based on modern, high-resolution, medical imaging techniques, the development of spatially realistic mathematical models for cardiovascular diseases, leads to complex systems of partial differential equations describing heterogeneous processes of multiscale nature. These coupled models require highly integrated and efficient numerical algorithms and high performance computing techniques for their simulation.
This special session will bring together open questions and recent advances in this topic.

Multi-scale Modeling and Homogenization of Partial Differential Equations

Hari Shankar Mahato
IIT Kharagpur, India

In this session, we focus on the multi-scale modeling of different types of physical phenomena. These phenomena usually give rise to partial differential equations. We will look into the analysis part of these PDEs such as existence and uniqueness of solution and we will also learn about different upscaling methods to homogenize these PDEs from micro-scale to macro-scale.

Recent Progress in the Theory of the Navier-Stokes and Related Equations

Sarka Necasova
Czech Academy of Sciences, Czech Republic

Jiri Neustupa
Czech Academy of Sciences, Czech Republic

The Navier-Stokes and related equations have already for many decades been a subject of great interest of mathematicians and physicists. 
Recently developed theoretical methods and tools enabled to formulate new criteria for uniqueness, stability, long time behavior and regularity of weak and mild solutions. New results also concern multi-component flows, interaction between fluids and immersed bodies and many other states or processes. 
The special session therefore aims at bringing together researchers from various countries, working in these or related fields, and to initiate or maintain fruitful discussions and cooperations.