Solutions to a One-Dimensional Combustion-Type Free Boundary Problem via Maximal Regularity

Furukawa, Ken; Giga, Yoshikazu; Kajiwara, Naoto

Hokkaido University Preprint Series in Mathematics, 2026, 1167(1), 1-26

Permalink : https://doi.org/10.14943/2115.100277

このアイテムのアクセス数:17件（2026-09-22 07:28 集計）

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アクセス権	open access
DOI	https://doi.org/10.14943/2115.100277
URI	https://hdl.handle.net/2115/100277
タイトル	Solutions to a One-Dimensional Combustion-Type Free Boundary Problem via Maximal Regularity
著者	Furukawa, Ken ; Giga, Yoshikazu ; Kajiwara, Naoto
著者名 Furukawa, Ken
著者名 Giga, Yoshikazu
著者名 Kajiwara, Naoto
言語	英語
発行日	2026-08-25
出版者	Department of Mathematics,Hokkaido University
収録物名	Hokkaido University Preprint Series in Mathematics
巻(号)	1167(1)
ページ	1-26
抄録	We study a one-dimensional free boundary problem arising in combustion theory, where the motion of the interface is governed by a prescribed Neumann boundary flux and a zero Dirichlet boundary condition. We treat both the half-line case and the bounded interval case. For both settings, we employ maximal Lp-Lq regularity as our main analytical tool. In the half-line case, the solutions need not decay at infinity, even though the spatial derivatives belong to Lq(R+). To handle the evolution law of the free boundary, we introduce a derivative formulation that avoids second-order boundary traces. By combining maximal Lp-Lq regularity and Schauder estimates, we establish the local-in-time existence, uniqueness, and regularity of solutions, as well as the evolution law of the free boundary.
資源タイプ	紀要論文
出版タイプ	Version of Record