| 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 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
140 |
| Issue:
|
2 |
| Year:
|
2015 |
| Pages:
|
129-137 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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 |
| DOI:
|
10.21136/MB.2015.144321 |
| . |
| Date available:
|
2015-06-30T12:12:17Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144321 |
| . |
| 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 |
| . |
