This paper deals with the chemotaxis-growth system: , , in a smooth bounded domain with zero-flux boundary conditions, where μ, δ, and τ are given positive parameters. It is shown that the solution exponentially stabilizes to the constant stationary solution in the norm of as provided that and any given nonnegative and suitably smooth initial data fulfills , which extends the condition in [8].
Cette Note traite du système de croissance chimiotaxique : , , dans un domaine borné lisse avec une condition de flux zéro au bord et où μ, δ et τ sont des paramètres positifs donnés. Nous montrons que la solution se stabilise exponentiellement vers la solution constante stationnaire en norme lorsque t tend vers l'infini, pourvu que et que toute donnée initiale positive ou nulle suffisamment lisse satisfasse . Ces hypothèses relaxent la condition de [8].
Accepted:
Published online:
Ya Tian 1; Dan Li 2; Chunlai Mu 3
@article{CRMATH_2019__357_6_513_0, author = {Ya Tian and Dan Li and Chunlai Mu}, title = {Stabilization in three-dimensional chemotaxis-growth model with indirect attractant production}, journal = {Comptes Rendus. Math\'ematique}, pages = {513--519}, publisher = {Elsevier}, volume = {357}, number = {6}, year = {2019}, doi = {10.1016/j.crma.2019.05.010}, language = {en}, }
TY - JOUR AU - Ya Tian AU - Dan Li AU - Chunlai Mu TI - Stabilization in three-dimensional chemotaxis-growth model with indirect attractant production JO - Comptes Rendus. Mathématique PY - 2019 SP - 513 EP - 519 VL - 357 IS - 6 PB - Elsevier DO - 10.1016/j.crma.2019.05.010 LA - en ID - CRMATH_2019__357_6_513_0 ER -
Ya Tian; Dan Li; Chunlai Mu. Stabilization in three-dimensional chemotaxis-growth model with indirect attractant production. Comptes Rendus. Mathématique, Volume 357 (2019) no. 6, pp. 513-519. doi : 10.1016/j.crma.2019.05.010. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2019.05.010/
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