Stochastic Model of Chemotaxis in System of Two Populations

A probabilistic representation of a weak solution to the Cauchy problem is constructed for a system of parabolic equations describing a chemotaxis process in a system of two interacting populations. A stochastic system describing the Keller–Segel type chemotaxis process and the Lotka–Volterra type i...

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Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 268; no. 5; pp. 555 - 572
Main Authors Belopolskaya, Ya. I, Nemchenko, E. I.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.12.2022
Springer
Springer Nature B.V
Subjects
Analysis
Cauchy problems
Differential equations
Existence theorems
Mathematics
Mathematics and Statistics
Populations
Stochastic models
Stochastic systems
Uniqueness theorems
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Summary:A probabilistic representation of a weak solution to the Cauchy problem is constructed for a system of parabolic equations describing a chemotaxis process in a system of two interacting populations. A stochastic system describing the Keller–Segel type chemotaxis process and the Lotka–Volterra type interaction between two populations is derived and existence and uniqueness theorem for its solution is proved. Finally, connections between solutions of the stochastic system and the Cauchy problem weak solution of the original PDE system are established.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-022-06227-7