LIOUVILLE-GREEN APPROXIMATION FOR LINEARLY COUPLED SYSTEMS: ASYMPTOTIC ANALYSIS WITH APPLICATIONS TO REACTION-DIFFUSION SYSTEMS
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F22%3A00363806" target="_blank" >RIV/68407700:21340/22:00363806 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.3934/dcdss.2022133" target="_blank" >https://doi.org/10.3934/dcdss.2022133</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3934/dcdss.2022133" target="_blank" >10.3934/dcdss.2022133</a>
Alternative languages
Result language
angličtina
Original language name
LIOUVILLE-GREEN APPROXIMATION FOR LINEARLY COUPLED SYSTEMS: ASYMPTOTIC ANALYSIS WITH APPLICATIONS TO REACTION-DIFFUSION SYSTEMS
Original language description
Asymptotic analysis has become a common approach in investigations of reaction-diffusion equations and pattern formation, especially when considering generalizations of the original model, such as spatial heterogeneity, where finding an analytic solution even to the linearized equations is generally not possible. The Liouville-Green approximation (also known as WKBJ method), one of the more robust asymptotic approaches for investigating dissipative phenomena captured by linear equations, has recently been applied to the Turing model in a heterogeneous environment. It demonstrated the anticipated modifications to the results obtained in a homogeneous setting, such as localized patterns and local Turing conditions. In this context, we attempt a generalization of the scalar Liouville-Green approximation to multicomponent systems. Our broader mathematical approach results in general approximation theorems for systems of ODEs without turning points. We discuss the cases of exponential and oscillatory behaviour first before treating the general case. Subsequently, we demonstrate the spectral properties utilized in the approximation theorems for a typical Turing system, hence showing that Liouville-Green approximation is plausible for an arbitrary number of coupled species outside of turning points and generally valid for fast growing modes as long as the diffusivities are distinct. Note that our line of approach is via showing that the solution is close (using suitable weight functions for measuring the error) to a linear combination of Airy-like functions.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
<a href="/en/project/GA20-22092S" target="_blank" >GA20-22092S: Multiscale thermodynamics: boundary conditions, integration and applications</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Discrete and Continuous Dynamical Systems. Series S
ISSN
1937-1632
e-ISSN
1937-1179
Volume of the periodical
15
Issue of the periodical within the volume
9
Country of publishing house
US - UNITED STATES
Number of pages
27
Pages from-to
2553-2579
UT code for WoS article
000824221100001
EID of the result in the Scopus database
2-s2.0-85135446156