Self-similar solutions for nonlinear Schrödinger equations.
Self-similar solutions for the two-dimensional Nernst-Planck-Debye system
We investigate the two-component Nernst-Planck-Debye system by a numerical study of self-similar solutions using the Runge-Kutta method of order four and comparing the results obtained with the solutions of a one-component system. Properties of the solutions indicated by numerical simulations are proved and an existence result is established based on comparison arguments for singular ordinary differential equations.
Self-similar solutions in reaction-diffusion systems
In this paper we examine self-similar solutions to the system , i = 1,…,m, , t > 0, , i = 1,…,m, , where m > 1 and , to describe asymptotics near the blow up point.
Self-similar solutions in weak Lp-spaces of the Navier-Stokes equations.
The most important result stated in this paper is a theorem on the existence of global solutions for the Navier-Stokes equations in Rn when the initial velocity belongs to the space weak Ln(Rn) with a sufficiently small norm. Furthermore, this fact leads us to obtain self-similar solutions if the initial velocity is, besides, an homogeneous function of degree -1. Partial uniqueness is also discussed.
Self-similar solutions of convection-diffusion processes.
Self-similarity in chemotaxis systems
We consider a system which describes the scaling limit of several chemotaxis systems. We focus on self-similarity, and review some recent results on forward and backward self-similar solutions to the system.
Self-similarly expanding networks to curve shortening flow
We consider a network in the Euclidean plane that consists of three distinct half-lines with common start points. From that network as initial condition, there exists a network that consists of three curves that all start at one point, where they form degree angles, and expands homothetically under curve shortening flow. We also prove uniqueness of these networks.
Semi-analytical approach to initial problems for systems of nonlinear partial differential equations with constant delay
This paper deals with the differential transform method for solving of an initial value problem for a system of two nonlinear functional partial differential equations of parabolic type. We consider non-delayed as well as delayed types of coupling and the different variety of initial functions are thought over. The convergence of solutions and the error estimation to the presented procedure is studied. Two numerical examples for non-delayed and delayed systems are included.
Semi-classical analysis and vanishing properties of solutions to quasilinear equations.
Semi-classical analysis for Harper's equation. III : Cantor structure of the spectrum
Semiclassical analysis of low lying eigenvalues. I. Non degenerate minima : asymptotic expansions
Semiclassical analysis of low lying eigenvalues. I. Non-degenerate minima : asymptotic expansions
Semiclassical and weak-magnetic-field eigenvalue asymptotics for the Schrödinger operator with electromagnetic potential
Semiclassical asymptotics for exchange energy
Semiclassical distribution of eigenvalues for elliptic operators with Hölder continuous coefficients, part i: non-critical case
We consider a version of the Weyl formula describing the asymptotic behaviour of the counting function of eigenvalues in the semiclassical approximation for self-adjoint elliptic differential operators under weak regularity hypotheses. Our aim is to treat Hölder continuous coefficients and to investigate the case of critical energy values as well.
Semi-classical eigenstates at the bottom of a multidimensional well
Semiclassical eigenstates in a multidimensional well
Semi-classical estimates for resolvents and asymptotics for total scattering cross-sections
Semiclassical expansion for the thermodynamic limit of the ground state energy of Kac's operator
We continue the study started by the first author of the semiclassical Kac Operator. This kind of operator has been obtained for example by M. Kac as he was studying a 2D spin lattice by the so-called “transfer operator method”. We are interested here in the thermodynamical limit of the ground state energy of this operator. For Kac’s spin model, is the free energy per spin, and the semiclassical regime corresponds to the mean-field approximation. Under suitable assumptions, which are satisfied...
Semiclassical fundamental solutions.