Pattern formation in hyperbolic models with cross-diffusion: Theory and applications
| Autor: | Carmela Currò, Giovanna Valenti |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Physics
Inertial frame of reference Hyperbolic model Extended thermodynamics Cross-diffusion Pattern formation Weakly nonlinear analysis Time evolution Pattern formation Statistical and Nonlinear Physics Context (language use) Condensed Matter Physics 01 natural sciences Stability (probability) 010305 fluids & plasmas Nonlinear system Amplitude 0103 physical sciences Statistical physics Transient (oscillation) 010306 general physics |
| Popis: | A class of hyperbolic reaction–diffusion models with cross-diffusion is derived within the context of Extended Thermodynamics. Linear stability analysis on the uniform steady states is performed to derive the conditions for the occurrence of Hopf, Turing and wave instabilities. The weakly nonlinear analysis is then employed to describe the time evolution of the pattern amplitude close to the stability threshold. The effects of the inertial times on the pattern formation as well as on the transient regimes are highlighted. As an illustrative example, our analysis is applied to the prototype Schnakenberg model and the theoretical results are illustrated both analytically and numerically. |
| Databáze: | OpenAIRE |
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