Sharp conditions on global existence and blow-up in a degenerate two-species and cross-attraction system

We consider a degenerate chemotaxis model with two-species and two-stimuli in dimension d ≥ 3 and find two critical curves intersecting at one point which separate the global existence and blow up of weak solutions to the problem. More precisely, above these curves (i.e. subcritical case), the probl...

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Autores principales:	Carrillo Antonio José, Lin Ke
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	degenerate parabolic system chemotaxis variational methods global existence blow up 35k65 92c17 35j20 35a01 35b44 Analysis QA299.6-433
Acceso en línea:	https://doaj.org/article/22fe78b727ba4dbc96658e2bba5eee83
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spelling	oai:doaj.org-article:22fe78b727ba4dbc96658e2bba5eee832021-12-05T14:10:40ZSharp conditions on global existence and blow-up in a degenerate two-species and cross-attraction system2191-94962191-950X10.1515/anona-2020-0189https://doaj.org/article/22fe78b727ba4dbc96658e2bba5eee832021-07-01T00:00:00Zhttps://doi.org/10.1515/anona-2020-0189https://doaj.org/toc/2191-9496https://doaj.org/toc/2191-950XWe consider a degenerate chemotaxis model with two-species and two-stimuli in dimension d ≥ 3 and find two critical curves intersecting at one point which separate the global existence and blow up of weak solutions to the problem. More precisely, above these curves (i.e. subcritical case), the problem admits a global weak solution obtained by the limits of strong solutions to an approximated system. Based on the second moment of solutions, initial data are constructed to make sure blow up occurs in finite time on and below these curves (i.e. critical and supercritical cases). In addition, the existence or non-existence of minimizers of free energy functional is discussed on the critical curves and the solutions exist globally in time if the size of initial data is small. We also investigate the crossing point between the critical lines in which a refined criteria in terms of the masses is given again to distinguish the dichotomy between global existence and blow up. We also show that the blow ups is simultaneous for both species.Carrillo Antonio JoséLin KeDe Gruyterarticledegenerate parabolic systemchemotaxisvariational methodsglobal existenceblow up35k6592c1735j2035a0135b44AnalysisQA299.6-433ENAdvances in Nonlinear Analysis, Vol 11, Iss 1, Pp 1-39 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	degenerate parabolic system chemotaxis variational methods global existence blow up 35k65 92c17 35j20 35a01 35b44 Analysis QA299.6-433
spellingShingle	degenerate parabolic system chemotaxis variational methods global existence blow up 35k65 92c17 35j20 35a01 35b44 Analysis QA299.6-433 Carrillo Antonio José Lin Ke Sharp conditions on global existence and blow-up in a degenerate two-species and cross-attraction system
description	We consider a degenerate chemotaxis model with two-species and two-stimuli in dimension d ≥ 3 and find two critical curves intersecting at one point which separate the global existence and blow up of weak solutions to the problem. More precisely, above these curves (i.e. subcritical case), the problem admits a global weak solution obtained by the limits of strong solutions to an approximated system. Based on the second moment of solutions, initial data are constructed to make sure blow up occurs in finite time on and below these curves (i.e. critical and supercritical cases). In addition, the existence or non-existence of minimizers of free energy functional is discussed on the critical curves and the solutions exist globally in time if the size of initial data is small. We also investigate the crossing point between the critical lines in which a refined criteria in terms of the masses is given again to distinguish the dichotomy between global existence and blow up. We also show that the blow ups is simultaneous for both species.
format	article
author	Carrillo Antonio José Lin Ke
author_facet	Carrillo Antonio José Lin Ke
author_sort	Carrillo Antonio José
title	Sharp conditions on global existence and blow-up in a degenerate two-species and cross-attraction system
title_short	Sharp conditions on global existence and blow-up in a degenerate two-species and cross-attraction system
title_full	Sharp conditions on global existence and blow-up in a degenerate two-species and cross-attraction system
title_fullStr	Sharp conditions on global existence and blow-up in a degenerate two-species and cross-attraction system
title_full_unstemmed	Sharp conditions on global existence and blow-up in a degenerate two-species and cross-attraction system
title_sort	sharp conditions on global existence and blow-up in a degenerate two-species and cross-attraction system
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/22fe78b727ba4dbc96658e2bba5eee83
work_keys_str_mv	AT carrilloantoniojose sharpconditionsonglobalexistenceandblowupinadegeneratetwospeciesandcrossattractionsystem AT linke sharpconditionsonglobalexistenceandblowupinadegeneratetwospeciesandcrossattractionsystem
_version_	1718371828827684864

Sharp conditions on global existence and blow-up in a degenerate two-species and cross-attraction system

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