On uniqueness  of a weak solution of one-dimensional concrete carbonation problem

Toyohiko Aiki; Adrian Muntean

doi:10.3934/dcds.2011.29.1345

Article Contents

2011, Volume 29, Issue 4: 1345-1365. Doi: 10.3934/dcds.2011.29.1345

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On uniqueness of a weak solution of one-dimensional concrete carbonation problem

Toyohiko Aiki^1, and
Adrian Muntean^2,

1.
Department of Mathematics, Faculty of Education, Gifu University, Yanagido 1-1, Gifu, 501-1193
2.
CASA - Centre for Analysis, Scientific computing and Applications, Department of Mathematics and Computer Science, Institute of Complex Molecular Systems, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven

Received: January 2010

Revised: August 2010

Published: October 2011

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Abstract

In our previous works we studied a one-dimensional free-boundary model related to the aggressive penetration of gaseous carbon dioxide in unsaturated concrete. Essentially, global existence and uniqueness of weak solutions to the model were obtained when the initial functions are bounded on the domain. In this paper we investigate the well-posedness of the problem for the case when the initial functions belong to a $L^2-$ class. Specifically, the uniqueness of weak solutions is proved by applying the dual equation method.

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Mathematics Subject Classification: Primary: 35R35; Secondary: 35B40, 76S05.

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References

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