New method for the existence and uniqueness of solution of nonlinear parabolic equation

• Main Authors: Wei, Li, Agarwal, Ravi P., Wong, Patricia Jia Yiing
• Other Authors: School of Electrical and Electronic Engineering
• Format: Article
• Language: English
• Published: 2015
• Subjects: H-monotone operator; Resolvent; Subdifferential; Parabolic equation
• Online Access: https://hdl.handle.net/10356/80992; http://hdl.handle.net/10220/39038
• Institution: Nanyang Technological University

There are two contributions in this paper. The first is that the abstract result for the existence of the unique solution of certain nonlinear parabolic equation is obtained by using the properties of H-monotone operators, consequently, the proof is simplified compared to the corresponding discussions in the literature. The second is that the connections between resolvent of H-monotone operators and solutions of nonlinear parabolic equations are shown, and this strengthens the importance of H-monotone operators, which have already attracted the attention of mathematicians because of the connections with practical problems.