| Title:
|
Time asymptotic description of an abstract Cauchy problem solution and application to transport equation (English) |
| Author:
|
Abdelmoumen, Boulbeba |
| Author:
|
Jedidi, Omar |
| Author:
|
Jeribi, Aref |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
59 |
| Issue:
|
1 |
| Year:
|
2014 |
| Pages:
|
53-67 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we study the time asymptotic behavior of the solution to an abstract Cauchy problem on Banach spaces without restriction on the initial data. The abstract results are then applied to the study of the time asymptotic behavior of solutions of an one-dimensional transport equation with boundary conditions in $L_1$-space arising in growing cell populations and originally introduced by M. Rotenberg, J. Theoret. Biol. 103 (1983), 181–199. (English) |
| Keyword:
|
evolution equation |
| Keyword:
|
semi-group |
| Keyword:
|
transport equation |
| Keyword:
|
perturbed semigroups |
| Keyword:
|
spectral theory |
| MSC:
|
20M10 |
| MSC:
|
35B40 |
| MSC:
|
35F10 |
| MSC:
|
35R20 |
| MSC:
|
47D06 |
| MSC:
|
82D75 |
| idZBL:
|
Zbl 06346372 |
| idMR:
|
MR3164576 |
| DOI:
|
10.1007/s10492-014-0041-y |
| . |
| Date available:
|
2014-01-28T13:56:20Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143598 |
| . |
| Reference:
|
[1] Abdelmoumen, B., Jeribi, A., Mnif, M.: Time asymptotic description of the solution to an abstract Cauchy problem and application to transport equation.Math. Z. 268 (2011), 837-869. Zbl 1231.47010, MR 2818733, 10.1007/s00209-010-0698-1 |
| Reference:
|
[2] Amar, A. Ben, Jeribi, A., Mnif, M.: Some applications of the regularity and irreducibility on transport theory.Acta Appl. Math. 110 (2010), 431-448. MR 2601665, 10.1007/s10440-009-9430-8 |
| Reference:
|
[3] Boulanouar, M.: A Rotenberg's model with perfect memory rule.C. R. Acad. Sci., Paris, Sér. I, Math. 327 (1998), 965-968 French. Zbl 0914.92014, MR 1659158 |
| Reference:
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[4] Dunford, N., Pettis, B. J.: Linear operations on summable functions.Trans. Am. Math. Soc. 47 (1940), 323-392. Zbl 0023.32902, MR 0002020, 10.1090/S0002-9947-1940-0002020-4 |
| Reference:
|
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| Reference:
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| Reference:
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[7] Hille, E., Phillips, R. S.: Functional Analysis and Semi-Groups. rev. ed.Colloquium Publications 31 American Mathematical Society, Providence (1957); Functional Analysis and Semi-Groups. 3rd printing of rev. ed. of 1957 Colloquium Publications 31 American Mathematical Society, Providence (1974). MR 0089373 |
| Reference:
|
[8] Jeribi, A.: A characterization of the essential spectrum and applications.Boll. Unione Mat. Ital., Sez. B, Artic. Ric. Mat. 8 (2002), 805-825. Zbl 1099.47501, MR 1934382 |
| Reference:
|
[9] Jeribi, A.: Time asymptotic behaviour for unbounded linear operators arising in growing cell populations.Nonlinear Anal., Real World Appl. 4 (2003), 667-688. Zbl 1039.92033, MR 1978556 |
| Reference:
|
[10] Kato, T.: Perturbation Theory for Linear Operators. 2nd ed.Grundlehren der mathematischen Wissenschaften 132 Springer, Berlin (1976). Zbl 0342.47009, MR 0407617 |
| Reference:
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| Reference:
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| Reference:
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[13] Pazy, A.: Semigroups of Linear Operators and Applications to Partial Differential Equations.Applied Mathematical Sciences 44 Springer, New York (1983). Zbl 0516.47023, MR 0710486 |
| Reference:
|
[14] Rotenberg, M.: Transport theory for growing cell populations.J. Theor. Biol. 103 (1983), 181-199. MR 0713945, 10.1016/0022-5193(83)90024-3 |
| Reference:
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[15] Smul'yan, Y. L.: Completely continuous perturbations of operators.Dokl. Akad. Nauk SSSR (N.S.) 101 (1955), 35-38 Russian; Completely continuous perturbations of operators. Translat. by M. G. Arsove Am. Math. Soc., Transl., II. Ser. 10 (1958), 341-344. Zbl 0080.10603 |
| Reference:
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| . |
