Time asymptotic description of an abstract Cauchy problem solution and application to transport equation

Boulbeba Abdelmoumen; Omar Jedidi; Aref Jeribi

Applications of Mathematics (2014)

  • Volume: 59, Issue: 1, page 53-67
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Abdelmoumen, Boulbeba, Jedidi, Omar, and Jeribi, Aref. "Time asymptotic description of an abstract Cauchy problem solution and application to transport equation." Applications of Mathematics 59.1 (2014): 53-67. <http://eudml.org/doc/260819>.

@article{Abdelmoumen2014,
abstract = {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.},
author = {Abdelmoumen, Boulbeba, Jedidi, Omar, Jeribi, Aref},
journal = {Applications of Mathematics},
keywords = {evolution equation; semi-group; transport equation; perturbed semigroups; spectral theory; transport equation; perturbed semigroups; spectral theory; evolution equation},
language = {eng},
number = {1},
pages = {53-67},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Time asymptotic description of an abstract Cauchy problem solution and application to transport equation},
url = {http://eudml.org/doc/260819},
volume = {59},
year = {2014},
}

TY - JOUR
AU - Abdelmoumen, Boulbeba
AU - Jedidi, Omar
AU - Jeribi, Aref
TI - Time asymptotic description of an abstract Cauchy problem solution and application to transport equation
JO - Applications of Mathematics
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 1
SP - 53
EP - 67
AB - 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.
LA - eng
KW - evolution equation; semi-group; transport equation; perturbed semigroups; spectral theory; transport equation; perturbed semigroups; spectral theory; evolution equation
UR - http://eudml.org/doc/260819
ER -

References

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  3. Boulanouar, M., A Rotenberg's model with perfect memory rule, C. R. Acad. Sci., Paris, Sér. I, Math. 327 (1998), 965-968 French. (1998) Zbl0914.92014MR1659158
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  8. Jeribi, A., A characterization of the essential spectrum and applications, Boll. Unione Mat. Ital., Sez. B, Artic. Ric. Mat. 8 (2002), 805-825. (2002) Zbl1099.47501MR1934382
  9. Jeribi, A., Time asymptotic behaviour for unbounded linear operators arising in growing cell populations, Nonlinear Anal., Real World Appl. 4 (2003), 667-688. (2003) Zbl1039.92033MR1978556
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  12. Mokhtar-Kharroubi, M., Time asymptotic behaviour and compactness in transport theory, European J. Mech. B Fluids 11 (1992), 39-68. (1992) MR1151539
  13. Pazy, A., Semigroups of Linear Operators and Applications to Partial Differential Equations, Applied Mathematical Sciences 44 Springer, New York (1983). (1983) Zbl0516.47023MR0710486
  14. Rotenberg, M., 10.1016/0022-5193(83)90024-3, J. Theor. Biol. 103 (1983), 181-199. (1983) MR0713945DOI10.1016/0022-5193(83)90024-3
  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. (1958) Zbl0080.10603
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