A one dimensional free boundary problem for adsorption phenomena. (English) Zbl 1310.35246
Summary: In this paper we deal with a one-dimensional free boundary problem, which is a mathematical model for an adsorption phenomena appearing in concrete carbonation process. This model was proposed in line of previous studies of three dimensional concrete carbonation process. The main result in this paper is concerned with the existence and uniqueness of a time-local solution to the free boundary problem. This result will be obtained by means of the abstract theory of nonlinear evolution equations and Banach’s fixed point theorem, and especially, the maximum principle applied to our problem will play a very important role to obtain the uniform estimate to approximate solutions.
MSC:
35R35 | Free boundary problems for PDEs |
35K61 | Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations |
74F25 | Chemical and reactive effects in solid mechanics |
References:
[1] | A. Muntean, A moving-boundary problem for concrete carbonation: Global existence and uniqueness of solutions,, Journal of Mathematical Analysis and Applications, 350, 234 (2009) · Zbl 1152.92035 · doi:10.1016/j.jmaa.2008.09.044 |
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