Qiang Liu, Wanyu Zhu, Hailong Ye
Abstract:
In this article, we study initial-boundary problems for
fourth-order nonlinear parabolic equations modeling thin film growth with
Caputo-type time fractional derivative.
By means of the theory of abstract fractional calculus and
\(L^p-L^q\) estimates, we establish the existence and uniqueness of local
mild solutions in the spaces
\(C([0,T]; L^{\frac{\beta N}{2-\beta}}(\Omega))\) with \(1<\beta<2\).
Moreover, the local solutions can be extended globally if the initial
data is sufficiently small.
Submitted March 30, 2024. Published October 4, 2024.
Math Subject Classifications: 35G25, 35K90.
Key Words: Thin-film equation; Caputo fractional derivative; mild solution; Mittag-Leffler functions.
DOI: 10.58997/ejde.2024.58
Show me the PDF file (365 KB), TEX file for this article.
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Qiang Liu School of Mathematical Sciences Shenzhen University Shenzhen, 518060, China email: matliu@szu.edu.cn |
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Wanyu Zhu School of Mathematical Sciences Shenzhen University Shenzhen, 518060, China email: 2200201025@email.szu.edu.cn |
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Hailong Ye School of Mathematical Sciences Shenzhen University Shenzhen, 518060, China email: yhl@szu.edu.cn |
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