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An Application Of The Theory Of Scale Of Banach Spaces

100%

Dawidowski Ł.

Annales Mathematicae Silesianae

2015

tom 29

nr 1

51-59

The abstract Cauchy problem on scales of Banach space was considered by many authors. The goal of this paper is to show that the choice of the space on scale is significant. We prove a theorem that the selection of the spaces in which the Cauchy problem ut − Δu = u|u|s with initial–boundary conditions is considered has an influence on the selection of index s. For the Cauchy problem connected with the heat equation we will study how the change of the base space influents the regularity of the solutions.

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A continuum individual based model of fragmentation: dynamics of correlation functions

61%

Tanaś A.

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

2015

tom 69

nr 2

An individual-based model of an infinite system of point particles in Rd is proposed and studied. In this model, each particle at random produces a finite number of new particles and disappears afterwards. The phase space for this model is the set Γ of all locally finite subsets of Rd. The system's states are probability measures on Γ the Markov evolution of which is described in terms of their correlation functions in a scale of Banach spaces. The existence and uniqueness of solutions of the corresponding evolution equation are proved.

Ograniczanie wyników

1 Annales Mathematicae Silesianae

1 Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

1 Dawidowski Ł.

1 Tanaś A.

2 2015

Wyniki wyszukiwania

An Application Of The Theory Of Scale Of Banach Spaces

A continuum individual based model of fragmentation: dynamics of correlation functions