Energy classification in a nonstandard fourth‐order parabolic equation with a Navier boundary condition

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 bet...

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Bibliographic Details
Published inMathematical methods in the applied sciences Vol. 46; no. 4; pp. 3703 - 3720
Main Authors Liu, Bingchen, Sun, Xizheng, Wang, Yiming
Format Journal Article
LanguageEnglish
Published Freiburg Wiley Subscription Services, Inc 15.03.2023
Subjects
Applications of mathematics
asymptotic behavior
blow‐up
Boundary conditions
Classification
extinction
Fluid flow
higher order parabolic equation
Mathematical analysis
potential well method
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ISSN0170-4214
1099-1476
DOI10.1002/mma.8717

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Summary: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.”
Bibliography:Funding information
Shandong Provincial Natural Science Foundation of China (ZR2021MA003 and ZR2020MA020) and the Fundamental Research Funds for the Central Universities (202111016).
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ISSN:0170-4214
1099-1476
DOI:10.1002/mma.8717