Energy classification in a nonstandard fourth‐order parabolic equation with a Navier boundary condition. (11th September 2022)

• Record Type: Journal Article
• Authors: Liu, Bingchen; Sun, Xizheng; Wang, Yiming
• Is Part Of: Mathematical methods in the applied sciences. Volume 46:Number 4(2023)
• Page Start: 3703
• Page End: 3720
• Publication Date: 2022-09-11
• Subjects: asymptotic behavior -- blow‐up -- extinction -- higher order parabolic equation -- potential well method; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.8717
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : This paper deals with a fourth‐order parabolic equation involving variable exponents, subject to Navier boundary conditions. We firstly give an optimal classification on the initial energy for blow‐up or global solutions, which is characterized by the sign of the Nehari energy and the difference between the initial energy and the depth of the potential well. Then, large time estimates of solutions are obtained. The results of the paper extend and complete the ones in " Applied Mathematics Letters 78(2018)141–146."