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Semigroup Analysis of Structured Parasite Populations

J. Z. Farkas, D. M. Green, P. Hinow (2010)

Mathematical Modelling of Natural Phenomena

Motivated by structured parasite populations in aquaculture we consider a class of size-structured population models, where individuals may be recruited into the population with distributed states at birth. The mathematical model which describes the evolution of such a population is a first-order nonlinear partial integro-differential equation of hyperbolic type. First, we use positive perturbation arguments and utilise results from the spectral...

Semigroup approach to the Stefan problem with non-linear flux

Enrico Magenes, Claudio Verdi, Augusto Visintin (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Un problema di Stefan a due fasi con condizione di flusso non lineare sulla parte fissa della frontiera è affrontato mediante la teoria dei semigruppi di contrazione in L 1 . Si dimostra l'esistenza e l’unicità della soluzione nel senso di Crandall-Liggett e Bénilan.

Semigroup commutators under differences (II).

Nicholas Th. Varopoulos (1993)

Revista Matemática Iberoamericana

This is the second instalment of my previous paper with the same title, [1]. This paper consists of two different parts. The first part is devoted to improvements of the results developed in [1]. These improvements are described in section 0.1 below and developed in sections 1 to 5, and 9 to 10; they are in fact technically distinct from [1] and rely on a systematic use of microlocalisation in the context of Hörmander-Weyl calculus. These paragraphs can therefore be read quite independently from...

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.

Semilinear Cauchy Problems with Almost Sectorial Operators

Tomasz Dlotko (2007)

Bulletin of the Polish Academy of Sciences. Mathematics

Existence of a mild solution to a semilinear Cauchy problem with an almost sectorial operator is studied. Under additional regularity assumptions on the nonlinearity and initial data we also prove the existence of a classical solution to this problem. An example of a parabolic problem in Hölder spaces illustrates the abstract result.

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