Dynamical problems without initial conditions for elliptic-parabolic equations in spatial unbounded domains.
Dynamical properties for a relaxation scheme applied to a weakly damped non local nonlinear Schrödinger equation.
Dynamical Resonances and SSF Singularities for a Magnetic Schrödinger Operator
We consider the Hamiltonian H of a 3D spinless non-relativistic quantum particle subject to parallel constant magnetic and non-constant electric field. The operator H has infinitely many eigenvalues of infinite multiplicity embedded in its continuous spectrum. We perturb H by appropriate scalar potentials V and investigate the transformation of these embedded eigenvalues into resonances. First, we assume that the electric potentials are dilation-analytic with respect to the variable along the magnetic...
Dynamics and patterns of an activator-inhibitor model with cubic polynomial source
The dynamics of an activator-inhibitor model with general cubic polynomial source is investigated. Without diffusion, we consider the existence, stability and bifurcations of equilibria by both eigenvalue analysis and numerical methods. For the reaction-diffusion system, a Lyapunov functional is proposed to declare the global stability of constant steady states, moreover, the condition related to the activator source leading to Turing instability is obtained in the paper. In addition, taking the...
Dynamics of complex singularities in 1D nonlinear parabolic PDE's
We establish local-in-time smoothing of a simple model nonlinear parabolic PDE in a scale of weighted Bergman spaces on a strip provided the weights are not too singular. This constitutes a very strong smoothing property since an immediate consequence is that the PDE can "push away" an algebraic-type complex singularity provided that the order of the singularity is small enough.
Dynamics of Erythroid Progenitors and Erythroleukemia
The paper is devoted to mathematical modelling of erythropoiesis, production of red blood cells in the bone marrow. We discuss intra-cellular regulatory networks which determine self-renewal and differentiation of erythroid progenitors. In the case of excessive self-renewal, immature cells can fill the bone marrow resulting in the development of leukemia. We introduce a parameter characterizing the strength of mutation. Depending on its value, leukemia will or will not develop. The simplest...
Dynamics of one-resonant biholomorphisms
Our first main result is a construction of a simple formal normal form for holomorphic diffeomorphisms in whose differentials have one-dimensional family of resonances in the first eigenvalues, (but more resonances are allowed for other eigenvalues). Next, we provide invariants and give conditions for the existence of basins of attraction. Finally, we give applications and examples demonstrating the sharpness of our conditions.
Dynamics of Propagation Phenomena in Biological Pattern Formation
A large variety of complex spatio-temporal patterns emerge from the processes occurring in biological systems, one of them being the result of propagating phenomena. This wave-like structures can be modelled via reaction-diffusion equations. If a solution of a reaction-diffusion equation represents a travelling wave, the shape of the solution will be the same at all time and the speed of propagation of this shape will be a constant. Travelling wave solutions of reaction-diffusion systems have been...
Dynamique des points vortex dans une équation de Ginzburg-Landau complexe
On considère une équation de Ginzburg-Landau complexe dans le plan. On étudie un régime asymptotique à petit paramètre dans lequel les solutions comportent des singularités ponctuelles, appelées points vortex, et on détermine un système d’équations différentielles ordinaires du premier ordre décrivant la dynamique de ces points jusqu’au premier temps de collision.
Dynamique des tourbillons de vorticité pour l’équation de Ginzburg-Landau parabolique
Edge asymptotics on a skew cylinder: complex variable form
Effective saturation for composite porous media
This paper is devoted to the study of the homogenization of a porous medium, composed of different materials arranged in a periodic structure. This provides the profile of the saturation function for the limit material.
Effects of magnetic field and nonlinear temperature profile on Marangoni convection in micropolar fluid.
Effet régularisant microlocal analytique pour l’équation de Schrödinger
Effet régularisant pour les solutions de l’équation de Schrödinger dans un domaine extérieur
Eigencurves for a Steklov problem.
Eigencurves of the -Laplacian with weights and their asymptotic behavior.
Eigenvalue problems for degenerate nonlinear elliptic equations in anisotropic media.
Eigenvalue questions on some quasilinear elliptic problems
Eigenvalues of inequalities of reaction-diffusion type and destabilizing effect of unilateral conditions