TY - JOUR
T1 - Erratum to the paper The fast signal diffusion limit in a chemotaxis system with strong signal sensitivity (Mathematische Nachrichten, (2018), 291, 8-9, (1342-1355), 10.1002/mana.201700270)
AU - Mizukami, Masaaki
PY - 2019/5
Y1 - 2019/5
N2 - We became aware of mistakes in the proof of [, Theorem 1.3]. We would like to thank Professor Michael Winkler for pointing out these mistakes, and moreover, appreciated his modifying arguments in his joint paper with Professors Yulan Wang and Zhaoyin Xiang ([]). In the following notations of the paper are used. The estimate 1 (Formula presented.) obtained in Theorem 1.2, is correct under the condition that 휒0 > 2푘(푎+휂)푘−1/푛. However, we cannot attain Theorem 1.3 from this estimate; more precisely, in the proof of Lemma 4.1, it seems to be impossible to obtain a uniform-in-λ 퐶훼, 훼/2 -estimate for 푣휆 because λ is a coefficient of (푣휆)푡. Theorem 1.3 must be corrected as follows.
AB - We became aware of mistakes in the proof of [, Theorem 1.3]. We would like to thank Professor Michael Winkler for pointing out these mistakes, and moreover, appreciated his modifying arguments in his joint paper with Professors Yulan Wang and Zhaoyin Xiang ([]). In the following notations of the paper are used. The estimate 1 (Formula presented.) obtained in Theorem 1.2, is correct under the condition that 휒0 > 2푘(푎+휂)푘−1/푛. However, we cannot attain Theorem 1.3 from this estimate; more precisely, in the proof of Lemma 4.1, it seems to be impossible to obtain a uniform-in-λ 퐶훼, 훼/2 -estimate for 푣휆 because λ is a coefficient of (푣휆)푡. Theorem 1.3 must be corrected as follows.
KW - 35K51
KW - 92C17
KW - chemotaxis system with signal sensitivity
KW - parabolic-elliptic system
KW - parabolic-parabolic system
KW - Primary: 35A09; Secondary: 35J15
UR - http://www.scopus.com/inward/record.url?scp=85065079358&partnerID=8YFLogxK
U2 - 10.1002/mana.201800266
DO - 10.1002/mana.201800266
M3 - Comment/debate
AN - SCOPUS:85065079358
VL - 292
JO - Mathematische Nachrichten
JF - Mathematische Nachrichten
SN - 0025-584X
IS - 5
ER -