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Local and global
solvability for advection-diffusion equation on an evolving
surface with a boundary
Hajime Koba |
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Vol. 15 (2022), No. 7, 1617–1654
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Abstract |
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This paper considers the existence of local and global-in-time strong solutions to the advection-diffusion equation with variable coefficients on an evolving surface with a boundary. We apply both the maximal -in-time regularity for Hilbert space-valued functions and semigroup theory to construct local and global-in-time strong solutions to an evolution equation. Using the approach and our function spaces on the evolving surface, we show the existence of local and global-in-time strong solutions to the advection-diffusion equation. Moreover, we derive the asymptotic stability of the global-in-time strong solution. |
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Keywords
advection-diffusion equation with variable coefficients,
time-dependent Laplace–Beltrami operator, function spaces
on evolving surfaces, maximal $L^p$-regularity, asymptotic
stability
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Mathematical Subject Classification 2010
Primary: 35A01
Secondary: 35R01, 35R37, 47D06
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Milestones
Received: 3 May 2019
Revised: 2 February 2021
Accepted: 19 March 2021
Published: 5 December 2022
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Authors |
| Hajime Koba | |
| Graduate School of Engineering
Science Osaka University Osaka Japan |
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