Long-time behaviour of the correlated random walk system
Other authors
Publication date
2025-08ISSN
2163-2480
Abstract
In this work, we consider the so-called correlated random walk system (also known as correlated motion or persistent motion system), used in biological modelling, among other fields, such as chromatography. This is a linear system which can also be seen as a weakly damped wave equation with certain boundary conditions. We are interested in the long-time behaviour of its solutions. To be precise, we will prove that the decay of the solutions to this problem is of exponential form, where the optimal decay rate exponent is given by the dominant eigenvalue of the corresponding operator. This eigenvalue can be obtained as a particular solution of a system of transcendental equations. A complete description of the spectrum of the operator is provided, together with a comprehensive analysis of the corresponding eigenfunctions and their geometry.
Document Type
Article
Document version
Accepted version
Language
English
Subject (CDU)
51 - Mathematics
512 - Algebra
Keywords
Correlated random walk
Persisten random walk
Chromatography
Optimal decay rate
Dominant eigenvalue
Semigroup theory
Camí aleatori
Cromatografia
Valors propis
Pages
p.27
Publisher
American Institute of Mathematical Sciences
Is part of
Evolution Equations and Control Theory, 2025, 14(4)
Grant agreement number
info:eu-repo/grantAgreement/SUR del DEC/SGR/2021 SGR 01228
info:eu-repo/grantAgreement/MCI/PN I+D/PID2021-123903NB-I00
info:eu-repo/grantAgreement/MCI/PN I+D/RED2022-134784- T
info:eu-repo/grantAgreement/SUR del DEC/SGR/2021- SGR-00087
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Rights
© American Institute of Mathematical Sciences