Local weak solvability of a moving boundary problem describing swelling along a halfline

Kota Kumazaki; Adrian Muntean

doi:10.3934/nhm.2019018

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2019, Volume 14, Issue 3: 445-469. Doi: 10.3934/nhm.2019018

This issue Previous Article Next Article On the local and global existence of solutions to 1d transport equations with nonlocal velocity

Local weak solvability of a moving boundary problem describing swelling along a halfline

Kota Kumazaki^1, and
Adrian Muntean^2,

1.
Nagasaki University, Department of Education, 1-14, Bunkyo-cho, Nagasaki, 852-8521, Japan
2.
Karlstad University, Department of Mathematics and Computer Science, Universitetsgatan 2,651 88 Karlstad, Sweden

Received: April 30, 2018

Revised: January 31, 2019

Published: August 2019

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Abstract

We obtain the local well-posedness of a moving boundary problem that describes the swelling of a pocket of water within an infinitely thin elongated pore (i.e. on $ [a, +\infty), \ a>0 $). Our result involves fine a priori estimates of the moving boundary evolution, Banach fixed point arguments as well as an application of the general theory of evolution equations governed by subdifferentials.

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Mathematics Subject Classification: Primary: 35R35; Secondary: 35B45, 35K61.

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