Lectures in Nonlinear Analysis and Differential Equations

Lectures in Nonlinear Analysis and Differential Equations

Doctoral School in Mathematics and Computer Science

Department of Mathematics and Computer Science of the University of Calabria

~~April 20-24, 2020~~

The meeting is cancelled due to the Coronavirus outbreak

Introduction:

The Course is intended for doctoral students and young researchers interested in Nonlinear Analysis and Differential Equations.

Parallel to the Course, some talks given by some of the participants are foreseen.

The Course schedule is available here.

Course Lecturers:

Elaine Crooks, Swansea University, United Kingdom
Feliz Minhos, University of Evora, Portugal
Radu Precup, Babes-Bolyai University, Romania

Course Program:

Front propagation and singular limits, by Elaine Crooks
These lectures will centre on two themes in nonlinear PDE that arise in modelling in biology and are motivated by phenomena such as strong competition and spatial segregation in population dynamics and biological invasions. The first half of the course will be concerned with competition-diffusion models, starting with the role played by equilibria in the long-time behaviour of solutions, including the effect of the shape of the spatial domain and the boundary conditions, followed by a discussion of large -interaction limits and how such limits can be used to deduce information about the behaviour of the competition-diffusion system. The second half of the course will focus on propagating-front solutions of reaction-diffusion equations and systems, including speeds of fronts, linear determinacy, the role of convection, and some examples of front-propagation problems from biology and physics.
Introduction to some topological methods for nonlinear boundary value problems, by Feliz Minhos
The aim of this course is to present some techniques and topological methods to deal with nonlinear boundary value problems, along the following lectures plan:
1. Integral equations: Green functions. Fixed point theory.
2. Lower and upper solutions method: Introduction to lower and upper solutions method with some particular Boundary Value Problems. Nagumo condition and a priori estimates.
3. Existence, localization and multiplicity results.
Hybrid fixed point and variational methods, by Radu Precup
1. We present fixed point theorems for operators defined on a Cartesian product of sets under heterogeneous conditions on the factor sets and the operator components. The results combine Banach-Perov contraction principle with topological fixed point theorems of Monch type in strong and weak topologies. Applications are given to operator systems.
2. A vector notion of linking is introduced in order to obtain, via a minimax principle, the existence and componentwise localization of solutions to systems of gradient type. The new approach allows the energy functional to combine minimization properties with respect to some of the variables, and the mountain pass geometry for the others.

Sponsor:

The Course is founded by the Erasmus+ Programme.

Previous Editions:

The previous editions of the Course were hosted in 2014, 2016 and 2019.

If you have any question, please contact us at the address gennaro.infante[at]unical.it

Updated on 22/3/2020.