Geodesic
Time asymptotic description of an abstract Cauchy problem solution and application to transport equation
Applications of Mathematics, Tome 59 (2014) no. 1, pp. 53-67.

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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.
DOI : 10.1007/s10492-014-0041-y
Classification : 20M10, 35B40, 35F10, 35R20, 47D06, 82D75
Keywords: evolution equation; semi-group; transport equation; perturbed semigroups; spectral theory 
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Abdelmoumen, Boulbeba; Jedidi, Omar; Jeribi, Aref. Time asymptotic description of an abstract Cauchy problem solution and application to transport equation. Applications of Mathematics, Tome 59 (2014) no. 1, pp. 53-67. doi : 10.1007/s10492-014-0041-y. http://geodesic.mathdoc.fr/articles/10.1007/s10492-014-0041-y/

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