# Large-time asymptotics of moving-reaction interfaces involving nonlinear Henry's law and time-dependent Dirichlet data

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- Technische Universiteit Eindhoven
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EINDHOVEN UNIVERSITY OF TECHNOLOGY EINDHOVEN UNIVERSITY OF TECHNOLOGY Department of Mathematics and Computer Science CASA-Report 13-03 January 2013 Large-time asymptotics of moving-reaction interfaces involving nonlinear Henry’s law and time-dependent Dirichlet data by T. Aiki, A. Muntean Centre for Analysis, Scientific computing and Applications Department of Mathematics and Computer Science Eindhoven University of Technology P.O. Box 513 5600 MB Eindhoven, The Netherlands ISSN: 0926-4507 Large-time asymptotics of moving-reaction interfaces involving nonlinear Henry’s law and time-dependent Dirichlet data Toyohiko Aikia, Adrian Munteanb aDepartment of Mathematics, Faculty of Science, Tokyo Women’s University, 2-8-1 Mejirodai, Bunkyo-ku, Tokyo, 112-8681, Japan, email: [email protected] bCASA - Centre for Analysis, Scientific computing and Applications, Institute for Complex Molecular Systems (ICMS), Eindhoven University of Technology, PO Box 513, 5600 MB, Eindhoven, The Netherlands, email: [email protected] Abstract We study the large-time behavior of the free boundary position capturing the one-dimensional motion of the carbonation reaction front in concrete-based materials. We extend here our rigorous justification of the √ t-behavior of reaction penetration depths by including non-linear effects due to deviations from the classical Henry’s law and time-dependent Dirichlet data. Keywords: Free boundary problem, concrete carbonation, Henry’s law, large-time behavior, time-dependent Dirichlet data 2010 MSC: 35R35, 35B20, 76S05 1. Introduction In this paper, we deal with the following initial free-boundary value prob- lem: Find {s, u, v} such that Qs(T ) = {(t, x)|0 < x < s(t), 0 < t < T}, ut − (κ1ux)x = f(u, v) in Qs(T ), (1) vt − (κ2vx)x = −f(u, v) in Qs(T ), (2) u(t, 0) = g(t), v(t, 0) =

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