TY - JOUR
T1 - On a comparison theorem for parabolic equations with nonlinear boundary conditions
AU - Kita, Kosuke
AU - Ôtani, Mitsuharu
N1 - Funding Information:
The authors would like to thank the referees for carefully reading the manuscript and for giving constructive comments which substantially helped improve the quality of this article. Kosuke Kita was partially supported by Grant-in-Aid for JSPS Fellows # 20J11425 and Mitsuharu Ôtani was partly supported by the Grant-in-Aid for Scientific Research, # 18K03382, the Ministry of Education, Culture, Sports, Science and Technology, Japan.
Publisher Copyright:
© 2022 Kosuke Kita and Mitsuharu Ôtani, published by De Gruyter.
PY - 2022/1/1
Y1 - 2022/1/1
N2 - In this article, a new type of comparison theorem for some second-order nonlinear parabolic systems with nonlinear boundary conditions is given, which can cover classical linear boundary conditions, such as the homogeneous Dirichlet or Neumann boundary condition. The advantage of our comparison theorem over the classical ones lies in the fact that it enables us to compare two solutions satisfying different types of boundary conditions. As an application of our comparison theorem, we can give some new results on the existence of blow-up solutions of some parabolic equations and systems with nonlinear boundary conditions.
AB - In this article, a new type of comparison theorem for some second-order nonlinear parabolic systems with nonlinear boundary conditions is given, which can cover classical linear boundary conditions, such as the homogeneous Dirichlet or Neumann boundary condition. The advantage of our comparison theorem over the classical ones lies in the fact that it enables us to compare two solutions satisfying different types of boundary conditions. As an application of our comparison theorem, we can give some new results on the existence of blow-up solutions of some parabolic equations and systems with nonlinear boundary conditions.
KW - blow up
KW - comparison theorem
KW - nonlinear boundary conditions
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U2 - 10.1515/anona-2022-0239
DO - 10.1515/anona-2022-0239
M3 - Article
AN - SCOPUS:85127005860
SN - 2191-9496
VL - 11
SP - 1165
EP - 1181
JO - Advances in Nonlinear Analysis
JF - Advances in Nonlinear Analysis
IS - 1
ER -