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Scalar boundary value problems on junctions of thin rods and plates

R. Bunoiu, G. Cardone, S. A. Nazarov (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We derive asymptotic formulas for the solutions of the mixed boundary value problem for the Poisson equation on the union of a thin cylindrical plate and several thin cylindrical rods. One of the ends of each rod is set into a hole in the plate and the other one is supplied with the Dirichlet condition. The Neumann conditions are imposed on the whole remaining part of the boundary. Elements of the junction are assumed to have contrasting properties so that the small parameter, i.e. the relative...

Scattering for 1D cubic NLS and singular vortex dynamics

Valeria Banica, Luis Vega (2012)

Journal of the European Mathematical Society

We study the stability of self-similar solutions of the binormal flow, which is a model for the dynamics of vortex filaments in fluids and super-fluids. These particular solutions χ a ( t , x ) form a family of evolving regular curves in ℝ 3 that develop a singularity in finite time, indexed by a parameter a > 0 . We consider curves that are small regular perturbations of χ a ( t 0 , x ) for a fixed time t 0 . In particular, their curvature is not vanishing at infinity, so we are not in the context of known results of local existence...

s∗-compressibility of the discrete Hartree-Fock equation

Heinz-Jürgen Flad, Reinhold Schneider (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The Hartree-Fock equation is widely accepted as the basic model of electronic structure calculation which serves as a canonical starting point for more sophisticated many-particle models. We have studied the s∗-compressibility for Galerkin discretizations of the Hartree-Fock equation in wavelet bases. Our focus is on the compression of Galerkin matrices from nuclear Coulomb potentials and nonlinear terms in the Fock operator which hitherto has not been discussed in the literature. It can be shown...

s∗-compressibility of the discrete Hartree-Fock equation

Heinz-Jürgen Flad, Reinhold Schneider (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

The Hartree-Fock equation is widely accepted as the basic model of electronic structure calculation which serves as a canonical starting point for more sophisticated many-particle models. We have studied the s∗-compressibility for Galerkin discretizations of the Hartree-Fock equation in wavelet bases. Our focus is on the compression of Galerkin matrices from nuclear Coulomb potentials and nonlinear terms in the Fock operator which hitherto has not been discussed in the literature. It can be shown...

Selfadjoint Extensions for the Elasticity System in Shape Optimization

Serguei A. Nazarov, Jan Sokołowski (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

Two approaches are proposed to modelling of topological variations in elastic solids. The first approach is based on the theory of selfadjoint extensions of differential operators. In the second approach function spaces with separated asymptotics and point asymptotic conditions are introduced, and a variational formulation is established. For both approaches, accuracy estimates are derived.

Self-similar solutions for the two-dimensional Nernst-Planck-Debye system

Łukasz Paszkowski (2012)

Applicationes Mathematicae

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.

Solitary wave and other solutions for nonlinear heat equations

Anatoly Nikitin, Tetyana Barannyk (2004)

Open Mathematics

A number of explicit solutions for the heat equation with a polynomial non-linearity and for the Fisher equation is presented. An extended class of non-linear heat equations admitting solitary wave solutions is described. The generalization of the Fisher equation is proposed whose solutions propagate with arbitrary ad hoc fixed velocity.

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