We report on some recent striking results that involve nonlinear elliptic equations. We first show that the standard monotonicity assumption in the statement of the maximum principle is not necessary. Next, we consider several classes of problems driven by differential operators with variable exponent. We are concerned both with small and high perturbations and we establish concentration phenomena of the spectrum, either near the origin or at infinity.
We consider an immersed object moving at constant speed in calm water. The water is seen as an incompressible inviscid fluid and the flow is irrotationnal. The wave resistance is the drag force exerted by the fluid on the object. This force is due to the presence of the water/air interface (indeed, if there were... Read More
Blood flow will be discussed where both red blood cells (RBC) and white cells (active) dynamics will be described. A brief summary of single RBC dynamics will be briefly recalled and most of discussion will then focus on collective dynamics: (i) spontaneous formation of blood crystals, (ii) what is the difference between blood flow and... Read More
In this talk, we will study an homogeneous and non-homogeneous inverse problem in electrocardiology representing the heart, lungs surfaces, and torso model. Our goal is to reconstruct the electrical potentials on the surface of the heart from the information obtained non invasively on the torso surface. The existence and uniqueness of solution for the heart-torso... Read More
The aim of this lecture is to introduce, review and discuss similarity and pseudosimilarity solutions to a class of problems in physics and mechanics. These solutions has proved to play an important role in the development of mathematical theories as well as in numerical computational schemes. Most remarkable is that similarity and pseudosimilarity solutions are... Read More
We deal with some class of second order time evolutive equations involving nonlinearitiries with arbitrary growth. The natural setting of the work is Orlicz spaces. Young measure Solutions are also introduced to solve our problem.
Les systèmes de réaction-diffusion ont connu ces dix dernières années un net regain d’intérêt du fait que ces systèmes apparaissent dans de nombreux modèles en biologie, en chimie, en biochimie, en dynamique des populations et en sciences de l’environnement en général. De nombreux systèmes de réaction-diffusion évolutifs présentent naturellement les deux pro- propriétés suivantes :... Read More