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...
Saved in:
Published in | Journal of mathematical sciences (New York, N.Y.) Vol. 268; no. 5; pp. 555 - 572 |
---|---|
Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Cham
Springer International Publishing
01.12.2022
Springer Springer Nature B.V |
Subjects | |
Online Access | Get full text |
Cover
Loading…
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 |