This paper deals with the chemotaxis system with nonlinear signal secretion
under homogeneous Neumann boundary conditions in a bounded domain (). The diffusion function and the chemotactic sensitivity function are given by and for all with and . The nonlinear signal secretion function is supposed to satisfy with . Global boundedness of solution is established under the specific conditions:
The purpose of this work is to remove the upper bound of the diffusion condition assumed in [9], and we also give the necessary constraint , which is ignored in [9, Theorem 1.1].
Revised:
Accepted:
Published online:
Xu Pan 1; Liangchen Wang 1
@article{CRMATH_2021__359_2_161_0, author = {Xu Pan and Liangchen Wang}, title = {Improvement of conditions for boundedness in a fully parabolic chemotaxis system with nonlinear signal production}, journal = {Comptes Rendus. Math\'ematique}, pages = {161--168}, publisher = {Acad\'emie des sciences, Paris}, volume = {359}, number = {2}, year = {2021}, doi = {10.5802/crmath.148}, language = {en}, }
TY - JOUR AU - Xu Pan AU - Liangchen Wang TI - Improvement of conditions for boundedness in a fully parabolic chemotaxis system with nonlinear signal production JO - Comptes Rendus. Mathématique PY - 2021 SP - 161 EP - 168 VL - 359 IS - 2 PB - Académie des sciences, Paris DO - 10.5802/crmath.148 LA - en ID - CRMATH_2021__359_2_161_0 ER -
%0 Journal Article %A Xu Pan %A Liangchen Wang %T Improvement of conditions for boundedness in a fully parabolic chemotaxis system with nonlinear signal production %J Comptes Rendus. Mathématique %D 2021 %P 161-168 %V 359 %N 2 %I Académie des sciences, Paris %R 10.5802/crmath.148 %G en %F CRMATH_2021__359_2_161_0
Xu Pan; Liangchen Wang. Improvement of conditions for boundedness in a fully parabolic chemotaxis system with nonlinear signal production. Comptes Rendus. Mathématique, Volume 359 (2021) no. 2, pp. 161-168. doi : 10.5802/crmath.148. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.148/
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