Scattering, transformations spectrales et équations d'évolution non linéaire II
Semi-discrétisation en temps pour les équations d'évolution paraboliques lorsque l'opérateur dépend du temps
Semigroup formulation of Rothe's method: application to parabolic problems
A semilinear parabolic equation in a Banach space is considered. The purpose of this paper is to show the dependence of an error estimate for Rothe's method on the regularity of initial data. The proofs are done using a semigroup theory and Taylor spectral representation.
Smoothing effect and discretization in time to semilinear parabolic equations with nonsmooth data
The purpose of this paper is to derive the error estimates for discretization in time of a semilinear parabolic equation in a Banach space. The estimates are given in the norm of the space for when the initial condition is not regular.
Solvability of boundary value problems for operator-differential equations of mixed type: the degenerate case.
Some fast finite-difference solvers for two-dimensional evolutionary equations on special domains
The author proves the existence of the asymptotic error expansion to the Peaceman-Rachford finite-difference scheme for the first boundary value problem of the two-dimensional evolationary equation on the so-called uniform and nearly uniform domains. This expansion leads, by Richardson extrapolation, to a simple process for accelerating the convergence of the method. A numerical example is given.
Some generic properties of nonlinear second order diffusional type problem
We are interested of the Newton type mixed problem for the general second order semilinear evolution equation. Applying Nikolskij’s decomposition theorem and general Fredholm operator theory results, the present paper yields sufficient conditions for generic properties, surjectivity and bifurcation sets of the given problem.
Some remarks on time-dependent evolution systems in the hyperbolic case
Some Uniqueness and Growth Theorems in the Cauchy Problem for P utt + M ut + Nu = 0 in Hilbert Space.
Spectral analysis of long wavelength periodic waves and applications.
Stabilité et convergence des méthodes spectrales polynômiales. Application à l'équation d'advection
Stability and error estimates valid for infinite time, for strongly monotone and infinitely stiff evolution equations
Stability and saddle-point property for a linear autonomous functional parabolic equation
Stabilization of solutions of abstract parabolic equations
Straightening of a noncylindrical region and evolution equations
Sulle equazioni paraboliche semilineari di ordine arbitrario in uno spazio di Banach
Symmetrization in nonlinear parabolic equations