Solvability Analysis of the Nonlinear Integral Equations System Arising in the Logistic Dynamics Model in the Case of Piecewise Constant Kernels

被引：1

作者：

Nikolaev, M. V. ^{[1
,2
]}

Nikitin, A. A. ^{[1
,3
]}

Dieckmann, U. ^{[4
,5
,6
]}

机构：

[1] Lomonosov Moscow State Univ, Fac Computat Math & Cybernet, Moscow, Russia

[2] Moscow Ctr Fundamental & Appl Math, Moscow, Russia

[3] Russian Acad Sci, Trapeznikov Inst Control Sci, Moscow, Russia

[4] Grad Univ, Okinawa Inst Sci & Technol, Onna, Japan

[5] Int Inst Appl Syst Anal, Laxenburg, Austria

[6] Grad Univ Adv Studies, Hayama, Japan

来源：

DOKLADY MATHEMATICS | 2024年 / 109卷 / 01期

基金：

俄罗斯科学基金会;

关键词：

functional analysis; nonlinear integral equations; mathematical biology;

D O I：

10.1134/S1064562424701783

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A nonlinear integral equation arising from a parametric closure of the third spatial moment in the single-species model of logistic dynamics of U. Dieckmann and R. Law is analyzed. The case of piecewise constant kernels is studied, which is important for further computer modeling. Sufficient conditions are found that guarantee the existence of a nontrivial solution to the equilibrium equation. The use of constant kernels makes it possible to obtain more accurate results compared to earlier works, in particular, more accurate estimates for the L-1 norm of the solution and for the closure parameter are obtained.

引用

页码：33 / 37

页数：5

共 5 条

[1] Dieckmann U., 2000, The geometry of ecological interactions: simplifying spatial complexity, DOI [10.1017/CBO9780511525537, DOI 10.1017/CBO9780511525537]
[2] Krasnoselskii M.A., 1955, Uspekhi Mat. Nauk., V10, P123
[3] Law R., 2000, GEOMETRY ECOLOGICAL
[4] On moment closures for population dynamics in continuous space
Murrell, DJ
Dieckmann, U
Law, R
[J]. JOURNAL OF THEORETICAL BIOLOGY, 2004, 229 (03) : 421 - 432
[5] Application of the Leray-Schauder Principle to the Analysis of a Nonlinear Integral Equation
Nikolaev, M. V.
Nikitin, A. A.
[J]. DIFFERENTIAL EQUATIONS, 2019, 55 (09) : 1164 - 1173

← 1 →