Convergence dans de la solution de l’équation de Klein-Gordon vers celle de l’équation des ondes
Convergence estimate for second order Cauchy problems with a small parameter
We consider the second order initial value problem in a Hilbert space, which is a singular perturbation of a first order initial value problem. The difference of the solution and its singular limit is estimated in terms of the small parameter The coefficients are commuting self-adjoint operators and the estimates hold also for the semilinear problem.
Convergence of a continuous BGK model for initial boundary-value problems for conservation laws.
Convergence of a finite element method based on the dual variational formulation
Convergence of a non-local eikonal equation to anisotropic mean curvature motion. Application to dislocations dynamics
We prove the convergence at a large scale of a non-local first order equation to an anisotropic mean curvature motion. The equation is an eikonal-type equation with a velocity depending in a non-local way on the solution itself, which arises in the theory of dislocation dynamics. We show that if an anisotropic mean curvature motion is approximated by equations of this type then it is always of variational type, whereas the converse is true only in dimension two.
Convergence of an entropic semi-discretization for nonlinear Fokker-Planck equations in Rd
Convergence of discretized attractors for parabolic equations on the line.
Convergence of functionals and its applications to parabolic equations.
Convergence of minimax structures and continuation of critical points for singularly perturbed systems
In the recent literature, the phenomenon of phase separation for binary mixtures of Bose–Einstein condensates can be understood, from a mathematical point of view, as governed by the asymptotic limit of the stationary Gross–Pitaevskii system , as the interspecies scattering length goes to . For this system we consider the associated energy functionals , with -mass constraints, which limit (as ) is strongly irregular. For such functionals, we construct multiple critical points via a common...
Convergence of Rothe's method in Hölder spaces
The convergence of Rothe’s method in Hölder spaces is discussed. The obtained results are based on uniform boundedness of Rothe’s approximate solutions in Hölder spaces recently achieved by the first author. The convergence and its rate are derived inside a parabolic cylinder assuming an additional compatibility conditions.
Convergence of solutions of generalized Korteweg-de Vries-Burgers equations to those of first order equations
Convergence of the boundary control for the wave equation in domains with holes of critical size.
Convergence of the coincidence set in the homogenization of the obstacle problem
Convergence of the 'relativistic' heat equation to the heat equation as c → ∞.
We prove that the entropy solutions of the so-called relativistic heat equation converge to solutions of the heat equation as the speed of light c tends to ∞ for any initial condition u0 ≥ 0 in L1(RN) ∩ L∞(RN).
Convergence Rates of the POD–Greedy Method
Iterative approximation algorithms are successfully applied in parametric approximation tasks. In particular, reduced basis methods make use of the so-called Greedy algorithm for approximating solution sets of parametrized partial differential equations. Recently, a priori convergence rate statements for this algorithm have been given (Buffa et al. 2009, Binev et al. 2010). The goal of the current study is the extension to time-dependent problems, which are typically approximated using the POD–Greedy...
Convergence results for MHD system.
Convergence results for unbounded solutions of first order non-linear differential-functional equations
We consider the Cauchy problem in an unbounded region for equations of the type either or . We prove convergence of their difference analogues by means of recurrence inequalities in some wide classes of unbounded functions.
Convergence to a positive equilibrium for some nonlinear evolution equations in a ball.
Convergence to equilibria for a three-dimensional conserved phase-field system with memory.
Convergence to stationary solutions in a model of self-gravitating systems
We study convergence of solutions to stationary states in an astrophysical model of evolution of clouds of self-gravitating particles.