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

2018/04/30 by Kota Kumazaki, Adrian Muntean, Kumazaki, Kota +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.1804.11053

arxiv created 2018/04/30 · openalex publication_date 2018/04/30 · arxiv updated 2018/05/01 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

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. 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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