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Title: Exponential decay of a solution for some parabolic equation involving a time nonlocal term (English)
Author: Kumazaki, Kota
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959
Volume: 140
Issue: 2
Year: 2015
Pages: 129-137
Summary lang: English
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Category: math
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Summary: We consider the large time behavior of a solution of a parabolic type equation involving a nonlocal term depending on the unknown function. This equation is proposed as a mathematical model of carbon dioxide transport in concrete carbonation process, and we proved the existence, uniqueness and large time behavior of a solution of this model. In this paper, we derive the exponential decay estimate of the solution of this model under restricted boundary data and initial data. (English)
Keyword: large time behavior
Keyword: exponential decay
Keyword: nonlinear parabolic equation
MSC: 35B40
MSC: 35K20
MSC: 35K55
idZBL: Zbl 06486929
idMR: MR3368489
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Date available: 2015-06-30T12:12:17Z
Last updated: 2016-07-01
Stable URL: http://hdl.handle.net/10338.dmlcz/144321
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Reference: [1] Aiki, T., Kumazaki, K.: Mathematical model for hysteresis phenomenon in moisture transport in concrete carbonation process.Phys. B 407 (2012), 1424-1426. 10.1016/j.physb.2011.10.016
Reference: [2] Aiki, T., Kumazaki, K.: Well-posedness of a mathematical model for moisture transport appearing in concrete carbonation process.Adv. Math. Sci. Appl. 21 (2011), 361-381. Zbl 1282.35186, MR 2953123
Reference: [3] Barbu, V.: Nonlinear Semigroups and Differential Equations in Banach Spaces.Noordhoff International Publishing, Leyden (1976). Zbl 0328.47035, MR 0390843
Reference: [4] Kenmochi, N.: Solvability of nonlinear evolution equations with time-dependent constraints and applications.Bull. Fac. Educ., Chiba Univ., Part 2 30 (1981), 1-87. Zbl 0662.35054
Reference: [5] Kumazaki, K.: A mathematical model of carbon dioxide transport in concrete carbonation process.Discrete Contin. Dyn. Syst., Ser. S 7 (2014), 113-125. Zbl 1272.35122, MR 3082859, 10.3934/dcdss.2014.7.113
Reference: [6] Kumazaki, K.: Large time behavior of a solution of carbon dioxide transport model in concrete carbonation process.J. Differ. Equations 257 (2014), 2136-2158. Zbl 1297.35040, MR 3227293, 10.1016/j.jde.2014.05.032
Reference: [7] Ladyzhenskaya, O. A., Solonnikov, V. A., Ural'tseva, N. N.: Linear and Quasi-Linear Equations of Parabolic Type.American Mathematical Society Providence, USA (1968). Zbl 0174.15403
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