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On the unique solvability of a nonlocal phase separation problem for multicomponent systems

Jens A. Griepentrog (2004)

Banach Center Publications

A nonlocal model of phase separation in multicomponent systems is presented. It is derived from conservation principles and minimization of free energy containing a nonlocal part due to particle interaction. In contrast to the classical Cahn-Hilliard theory with higher order terms this leads to an evolution system of second order parabolic equations for the particle densities, coupled by nonlinear and nonlocal drift terms, and state equations which involve both chemical and interaction potential...

On the Volterra integral equation with weakly singular kernel

Stanisław Szufla (2006)

Mathematica Bohemica

We give sufficient conditions for the existence of at least one integrable solution of equation x ( t ) = f ( t ) + ∫ 0 t K ( t , s ) g ( s , x ( s ) ) d s . Our assumptions and proofs are expressed in terms of measures of noncompactness.

On three problems of neutron transport theory

Jan Kyncl (1986)

Aplikace matematiky

In this paper, the initial-value problem, the problem of asymptotic time behaviour of its solution and the problem of criticality are studied in the case of linear Boltzmann equation for both finite and infinite media. Space of functions where these problems are solved is chosen in such a vay that the range of physical situations considered may be so wide as possible. As mathematical apparatus the theory of positive bounded operators and of semigroups are applied. Main results are summarized in...

One-dimensional model describing the non-linear viscoelastic response of materials

Tomáš Bárta (2014)

Commentationes Mathematicae Universitatis Carolinae

In this paper we consider a model of a one-dimensional body where strain depends on the history of stress. We show local existence for large data and global existence for small data of classical solutions and convergence of the displacement, strain and stress to zero for time going to infinity.

Opérateurs intégro-différentiels méromorphes et opérateurs aux différences

Anne Duval (1987)

Annales de l'institut Fourier

On introduit une classe d’opérateurs intégro-différentiels d’ordre infini, à coefficients méromorphes et pour lesquels les séries majorantes sont de type Dirichlet. On établit des résultats algébriques : caractérisation des éléments inversibles, théorèmes de division et de préparation. En les faisant opérer sur divers espaces de séries et de fonctions on obtient des théorèmes d’indices et des résultats de surjectivité. Après transformation de Mellin ces opérateurs permettent d’étudier les “solutions”...

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