TY - JOUR
T1 - A computer-assisted method for the diblock copolymer model
AU - Cai, Shuting
AU - Watanabe, Yoshitaka
N1 - Funding Information:
Ministry of Education, Culture, Sports, Science and Technology, Grant/Award Number: 15H036367; National Natural Science Foundation of China, Grant/Award Number: 11501107; Core Research for Evolutional Science and Technology
Funding Information:
The present study was supported by the National Natural Science Foundation of China (No. 11501107) and a Grant-in-Aid from the Ministry of Education, Culture, Sports, Science and Technology of Japan (No. 15H03637) and CREST, JST.
Publisher Copyright:
© 2019 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
PY - 2019/7
Y1 - 2019/7
N2 - We propose a computer-assisted method by which to enclose a solution of the diblock copolymer model. We begin by using the Newton method to obtain a solution, and we then prove that the residual part of the approximation is a fixed point of a compact operator. Next, using a computer, we construct a set which satisfies the hypothesis of the Banach fixed-point theorem for the operator in a certain Sobolev space, which therefore contains a unique solution. Finally, we present some verified results.
AB - We propose a computer-assisted method by which to enclose a solution of the diblock copolymer model. We begin by using the Newton method to obtain a solution, and we then prove that the residual part of the approximation is a fixed point of a compact operator. Next, using a computer, we construct a set which satisfies the hypothesis of the Banach fixed-point theorem for the operator in a certain Sobolev space, which therefore contains a unique solution. Finally, we present some verified results.
UR - http://www.scopus.com/inward/record.url?scp=85065023590&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85065023590&partnerID=8YFLogxK
U2 - 10.1002/zamm.201800125
DO - 10.1002/zamm.201800125
M3 - Article
AN - SCOPUS:85065023590
SN - 0044-2267
VL - 99
JO - ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
JF - ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
IS - 7
M1 - e201800125
ER -