Characterization of Traveling Waves Solutions to an Heterogeneous Diffusion Coupled System with Weak Advection
The aim of this work is to characterize Traveling Waves (TW) solutions for a coupled system with KPP-Fisher nonlinearity and weak advection. The heterogeneous diffusion introduces certain instabilities in the TW heteroclinic connections that are explored. In addition, a weak advection reflects the e...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/18/2300 |
| _version_ | 1797518298167902208 |
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| author | José Luis Díaz Palencia |
| author_facet | José Luis Díaz Palencia |
| author_sort | José Luis Díaz Palencia |
| collection | DOAJ |
| description | The aim of this work is to characterize Traveling Waves (TW) solutions for a coupled system with KPP-Fisher nonlinearity and weak advection. The heterogeneous diffusion introduces certain instabilities in the TW heteroclinic connections that are explored. In addition, a weak advection reflects the existence of a critical combined TW speed for which solutions are purely monotone. This study follows purely analytical techniques together with numerical exercises used to validate or extent the contents of the analytical principles. The main concepts treated are related to positivity conditions, TW propagation speed and homotopy representations to characterize the TW asymptotic behaviour. |
| first_indexed | 2024-03-10T07:27:55Z |
| format | Article |
| id | doaj.art-46e8fef0840e405b84b7e39ecdad3ebd |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T07:27:55Z |
| publishDate | 2021-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-46e8fef0840e405b84b7e39ecdad3ebd2023-11-22T14:06:19ZengMDPI AGMathematics2227-73902021-09-01918230010.3390/math9182300Characterization of Traveling Waves Solutions to an Heterogeneous Diffusion Coupled System with Weak AdvectionJosé Luis Díaz Palencia0Escuela Politécnica Superior, Universidad Francisco de Vitoria, Ctra. Pozuelo-Majadahonda Km 1800, Pozuelo de Alarcón, 28223 Madrid, SpainThe aim of this work is to characterize Traveling Waves (TW) solutions for a coupled system with KPP-Fisher nonlinearity and weak advection. The heterogeneous diffusion introduces certain instabilities in the TW heteroclinic connections that are explored. In addition, a weak advection reflects the existence of a critical combined TW speed for which solutions are purely monotone. This study follows purely analytical techniques together with numerical exercises used to validate or extent the contents of the analytical principles. The main concepts treated are related to positivity conditions, TW propagation speed and homotopy representations to characterize the TW asymptotic behaviour.https://www.mdpi.com/2227-7390/9/18/2300positivity in heterogeneous diffusiontraveling wavesasymptotic homotopy |
| spellingShingle | José Luis Díaz Palencia Characterization of Traveling Waves Solutions to an Heterogeneous Diffusion Coupled System with Weak Advection Mathematics positivity in heterogeneous diffusion traveling waves asymptotic homotopy |
| title | Characterization of Traveling Waves Solutions to an Heterogeneous Diffusion Coupled System with Weak Advection |
| title_full | Characterization of Traveling Waves Solutions to an Heterogeneous Diffusion Coupled System with Weak Advection |
| title_fullStr | Characterization of Traveling Waves Solutions to an Heterogeneous Diffusion Coupled System with Weak Advection |
| title_full_unstemmed | Characterization of Traveling Waves Solutions to an Heterogeneous Diffusion Coupled System with Weak Advection |
| title_short | Characterization of Traveling Waves Solutions to an Heterogeneous Diffusion Coupled System with Weak Advection |
| title_sort | characterization of traveling waves solutions to an heterogeneous diffusion coupled system with weak advection |
| topic | positivity in heterogeneous diffusion traveling waves asymptotic homotopy |
| url | https://www.mdpi.com/2227-7390/9/18/2300 |
| work_keys_str_mv | AT joseluisdiazpalencia characterizationoftravelingwavessolutionstoanheterogeneousdiffusioncoupledsystemwithweakadvection |