Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 10, 3371–3670
Issue 9, 2997–3369
Issue 8, 2619–2996
Issue 7, 2247–2618
Issue 6, 1871–2245
Issue 5, 1501–1870
Issue 4, 1127–1500
Issue 3, 757–1126
Issue 2, 379–756
Issue 1, 1–377

Volume 16, 10 issues

Volume 15, 8 issues

Volume 14, 8 issues

Volume 13, 8 issues

Volume 12, 8 issues

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
ISSN 1948-206X (online)
ISSN 2157-5045 (print)
 
Author index
To appear
 
Other MSP journals
Local and global solvability for advection-diffusion equation on an evolving surface with a boundary

Hajime Koba

Vol. 15 (2022), No. 7, 1617–1654
Abstract

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 Lp-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.

Keywords
advection-diffusion equation with variable coefficients, time-dependent Laplace–Beltrami operator, function spaces on evolving surfaces, maximal $L^p$-regularity, asymptotic stability
Mathematical Subject Classification 2010
Primary: 35A01
Secondary: 35R01, 35R37, 47D06
Milestones
Received: 3 May 2019
Revised: 2 February 2021
Accepted: 19 March 2021
Published: 5 December 2022
Authors
Hajime Koba
Graduate School of Engineering Science
Osaka University
Osaka
Japan