On the pressureless damped Euler-Poisson equations with quadratic confinement: critical thresholds and large-time behavior
We analyze the one-dimensional pressureless Euler-Poisson equations with linear damping and nonlocal interaction forces. These equations are relevant for modeling collective behavior in mathematical biology. We provide a sharp threshold between the supercritical region with finite-time breakdown and...
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| Format: | Journal article |
| Language: | English |
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World Scientific Publishing
2016
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| _version_ | 1826272975480946688 |
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| author | Carrillo. JA Choi, Y-P Zatorska, E |
| author_facet | Carrillo. JA Choi, Y-P Zatorska, E |
| author_sort | Carrillo. JA |
| collection | OXFORD |
| description | We analyze the one-dimensional pressureless Euler-Poisson equations with linear damping and nonlocal interaction forces. These equations are relevant for modeling collective behavior in mathematical biology. We provide a sharp threshold between the supercritical region with finite-time breakdown and the subcritical region with global-in-time existence of the classical solution. We derive an explicit form of solution in Lagrangian coordinates which enables us to study the time-asymptotic behavior of classical solutions with the initial data in the subcritical region. |
| first_indexed | 2024-03-06T22:21:03Z |
| format | Journal article |
| id | oxford-uuid:5511d696-c9fe-4a76-aaa2-7ca02bb68041 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T22:21:03Z |
| publishDate | 2016 |
| publisher | World Scientific Publishing |
| record_format | dspace |
| spelling | oxford-uuid:5511d696-c9fe-4a76-aaa2-7ca02bb680412022-03-26T16:41:44ZOn the pressureless damped Euler-Poisson equations with quadratic confinement: critical thresholds and large-time behaviorJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:5511d696-c9fe-4a76-aaa2-7ca02bb68041EnglishSymplectic ElementsWorld Scientific Publishing2016Carrillo. JAChoi, Y-PZatorska, EWe analyze the one-dimensional pressureless Euler-Poisson equations with linear damping and nonlocal interaction forces. These equations are relevant for modeling collective behavior in mathematical biology. We provide a sharp threshold between the supercritical region with finite-time breakdown and the subcritical region with global-in-time existence of the classical solution. We derive an explicit form of solution in Lagrangian coordinates which enables us to study the time-asymptotic behavior of classical solutions with the initial data in the subcritical region. |
| spellingShingle | Carrillo. JA Choi, Y-P Zatorska, E On the pressureless damped Euler-Poisson equations with quadratic confinement: critical thresholds and large-time behavior |
| title | On the pressureless damped Euler-Poisson equations with quadratic confinement: critical thresholds and large-time behavior |
| title_full | On the pressureless damped Euler-Poisson equations with quadratic confinement: critical thresholds and large-time behavior |
| title_fullStr | On the pressureless damped Euler-Poisson equations with quadratic confinement: critical thresholds and large-time behavior |
| title_full_unstemmed | On the pressureless damped Euler-Poisson equations with quadratic confinement: critical thresholds and large-time behavior |
| title_short | On the pressureless damped Euler-Poisson equations with quadratic confinement: critical thresholds and large-time behavior |
| title_sort | on the pressureless damped euler poisson equations with quadratic confinement critical thresholds and large time behavior |
| work_keys_str_mv | AT carrilloja onthepressurelessdampedeulerpoissonequationswithquadraticconfinementcriticalthresholdsandlargetimebehavior AT choiyp onthepressurelessdampedeulerpoissonequationswithquadraticconfinementcriticalthresholdsandlargetimebehavior AT zatorskae onthepressurelessdampedeulerpoissonequationswithquadraticconfinementcriticalthresholdsandlargetimebehavior |