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Semigroup formulation of Rothe's method: application to parabolic problems

Marián Slodička (1992)

Commentationes Mathematicae Universitatis Carolinae

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.

Some fast finite-difference solvers for two-dimensional evolutionary equations on special domains

Ta Van Dinh (1982)

Aplikace matematiky

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

Vladimír Ďurikovič, Mária Ďurikovičová (1999)

Archivum Mathematicum

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.

The Cauchy problem for systems through the normal form of systems and theory of weighted determinant

Waichiro Matsumoto (1998/1999)

Séminaire Équations aux dérivées partielles

The author propose what is the principal part of linear systems of partial differential equations in the Cauchy problem through the normal form of systems in the meromorphic formal symbol class and the theory of weighted determinant. As applications, he choose the necessary and sufficient conditions for the analytic well-posedness ( Cauchy-Kowalevskaya theorem ) and C well-posedness (Levi condition).

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