Long-time behaviour of the correlated random walk system
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...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/440005 |
| Acceso en línea: | https://hdl.handle.net/2117/440005 https://dx.doi.org/10.3934/eect.2025009 |
| Access Level: | acceso abierto |
| Palabra clave: | Differential equations, Partial Mathematical models Random walks Correlated random walk Persisten random walk Chromatography Optimal decay rate Dominant eigenvalue Semigroup theory Equacions diferencials parcials Models matemàtics Rutes aleatòries (Matemàtica) Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica Àrees temàtiques de la UPC::Física::Termodinàmica |
| Sumario: | 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. |
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