Periodic solutions of partial differential equations with hysteresis
Perona-Malik equation: properties of explicit finite volume scheme
The Perona–Malik nonlinear parabolic problem, which is widely used in image processing, is investigated in this paper from the numerical point of view. An explicit finite volume numerical scheme for this problem is presented and consistency property is proved.
Post-buckling range of plates in axial compression with uncertain initial geometric imperfections
The method of reliable solutions alias the worst scenario method is applied to the problem of von Kármán equations with uncertain initial deflection. Assuming two-mode initial and total deflections and using Galerkin approximations, the analysis leads to a system of two nonlinear algebraic equations with one or two uncertain parameters-amplitudes of initial deflections. Numerical examples involve (i) minimization of lower buckling loads and (ii) maximization of the maximal mean reduced stress.
Quasilinear problems with singularities.
Quasi-linearisation methods for a nonlinear heat equation with functional dependence.
Quasilinearization for some nonlocal problems.
Quasireversibility for inhomogeneous ill-posed problems in Hilbert spaces.
Quasireversibility methods for non-well-posed problems.
Quenching semidiscretizations in time of a nonlocal parabolic problem with Neumann boundary condition.
Reaction diffusion equations and quadratic convergence.
Reflectionless boundary propagation formulas for partial wave solutions to the wave equation.
Reproducing kernel methods for solving linear initial-boundary-value problems.
Robust a priori error analysis for the approximation of degree-one Ginzburg-Landau vortices
This article discusses the numerical approximation of time dependent Ginzburg-Landau equations. Optimal error estimates which are robust with respect to a large Ginzburg-Landau parameter are established for a semi-discrete in time and a fully discrete approximation scheme. The proofs rely on an asymptotic expansion of the exact solution and a stability result for degree-one Ginzburg-Landau vortices. The error bounds prove that degree-one vortices can be approximated robustly while unstable higher...
Robust a priori error analysis for the approximation of degree-one Ginzburg-Landau vortices
This article discusses the numerical approximation of time dependent Ginzburg-Landau equations. Optimal error estimates which are robust with respect to a large Ginzburg-Landau parameter are established for a semi-discrete in time and a fully discrete approximation scheme. The proofs rely on an asymptotic expansion of the exact solution and a stability result for degree-one Ginzburg-Landau vortices. The error bounds prove that degree-one vortices can be approximated robustly while unstable higher...
Rothe method for a mixed problem with an integral condition for the two-dimensional diffusion equation.
Rothe time-discretization method for a nonlocal problem arising in thermoelasticity.
Runge Property and Multiplicity of Solutions for Elliptic Equations in IRN with a Monotone Nonlinearity.
Scattering amplitude for the Schrödinger equation with strong magnetic field
In this note, we study the scattering amplitude for the Schrödinger equation with constant magnetic field. We consider the case where the strengh of the magnetic field goes to infinity and we discuss the competition between the magnetic and the electrostatic effects.
Schéma des différences finies pour un système d'équations non linéaires partielles elliptiques aux dérivées mixtes et avec des conditions aux limites du type de Neumann
Second-order boundary estimates for solutions to singular elliptic equations in borderline cases.