A free boundary problem with two moving boundaries modeling grain hydration. (27th June 2018)

• Record Type: Journal Article
• Authors: Pan, Hongjing; Xing, Ruixiang; Hu, Bei
• Is Part Of: Nonlinearity. Volume 31:Number 8(2018:Aug.)
• Page Start: 3591
• Page End: 3616
• Publication Date: 2018-06-27
• Subjects: one-phase Stefan problem -- moving boundary problem -- asymptotic behavior -- free boundary problem -- grain swelling; 35R35 -- 35R37 -- 74N20 -- 76S05 -- 80A22; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/aabf04
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: In this paper, we study a free boundary problem modeling grain hydration. The grain is submersed in water, and there are two free boundaries occurring in this problem. The outer free boundary is the boundary separating the grain region from water region . The inner boundary is the boundary separating the wet region from the dry region . Water penetrates from water region into grain region and also from wet region into dry region—causing both free boundaries to move. We show that this problem globally in time is well posed, and admits a unique solution with two stages. We prove that there exists a such that the inner free boundary reaches the origin at T * : S ( T * − 0) = 0. The problem on the time interval [0, T * ] constitutes stage I and on the time interval constitutes stage II. We establish that, and that (the saturated moisture content). The solution is singular at time t = 0; we give an explicit characteristics of singularity at t = 0. The solution is also singular near point (0, T * ); we shall use approximation to study the behavior of the solution.