TY - JOUR
T1 - Regular solutions of chemotaxis-consumption systems involving tensor-valued sensitivities and Robin type boundary conditions
AU - Ahn, Jaewook
AU - Kang, Kyungkeun
AU - Lee, Jihoon
N1 - Publisher Copyright:
© 2023 World Scientific Publishing Company.
PY - 2023/10/1
Y1 - 2023/10/1
N2 - This paper deals with a parabolic-elliptic chemotaxis-consumption system with tensor-valued sensitivity S(x,n,c) under no-flux boundary conditions for n and Robin-type boundary conditions for c. The global existence of bounded classical solutions is established in dimension two under general assumptions on tensor-valued sensitivity S. One of the main steps is to show that ∇c(·, t) becomes tiny in L2(Br(x) ∩ ω¯) for every x ω¯ and t when r is sufficiently small, which seems to be of independent interest. On the other hand, in the case of scalar-valued sensitivity S = χ(x,n,c)I, there exists a bounded classical solution globally in time for two and higher dimensions provided the domain is a ball with radius R and all given data are radial. The result of the radial case covers scalar-valued sensitivity χ that can be singular at c = 0.
AB - This paper deals with a parabolic-elliptic chemotaxis-consumption system with tensor-valued sensitivity S(x,n,c) under no-flux boundary conditions for n and Robin-type boundary conditions for c. The global existence of bounded classical solutions is established in dimension two under general assumptions on tensor-valued sensitivity S. One of the main steps is to show that ∇c(·, t) becomes tiny in L2(Br(x) ∩ ω¯) for every x ω¯ and t when r is sufficiently small, which seems to be of independent interest. On the other hand, in the case of scalar-valued sensitivity S = χ(x,n,c)I, there exists a bounded classical solution globally in time for two and higher dimensions provided the domain is a ball with radius R and all given data are radial. The result of the radial case covers scalar-valued sensitivity χ that can be singular at c = 0.
KW - Chemotaxis-consumption system
KW - regular solution
KW - Robin-type boundary condition
KW - tensor-valued sensitivity
UR - http://www.scopus.com/inward/record.url?scp=85166031482&partnerID=8YFLogxK
U2 - 10.1142/S0218202523400055
DO - 10.1142/S0218202523400055
M3 - Article
AN - SCOPUS:85166031482
SN - 0218-2025
VL - 33
SP - 2337
EP - 2360
JO - Mathematical Models and Methods in Applied Sciences
JF - Mathematical Models and Methods in Applied Sciences
IS - 11
ER -