Existence results for a boundary value problem arising in growing cell populations

Mathematical Models and Methods in Applied Sciences

Volumn 13, Issue 1, 2003, Pages 1-17

  Latrach, Khalid ^a   Zeghal, Ahmed ^b  

^a UNIVERSITÉ DE CORSE   (France)

^b FACULTÉ DES SCIENCES ET TECHNIQUES GUÉLIZ   (Morocco)

Author keywords

Boundary value problem; Dunford Pettis weak compactness criteria; Fixed point theorems; Transport equation

Indexed keywords

EID: 0037289422     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202503002350     Document Type: Article

References (16)

1. L. Arlotti, N. Bellomo and E. De Engelis, Generalized kinetic (Boltzmann) models, mathematical structures and applications, Math. Models Methods Appl. Sci. 12 (2002) 569-596.
2. L. Arlotti, N. Bellomo and K. Latrach, From the Jager and Segel model to kinetic population dynamics nonlinear evolution problems and applications, Math. Comp. Modelling 30 (1999) 15-40.
3. R. Dautray and J. L. Lions, Analyse Mathématique et Calcul Numérique, Vol. 9 (Masson, 1988).
4. A. Dehici, A. Jeribi and K. Latrach, On a transport operator arising in growing cell populations I. Spectral analysis, Advances in Math. Research, ed. G. Oyibo (Nova Sci. Publishers, 2002), pp. 159-186.
5. J. Dugundji and A. Granas, Fixed Point Theory (PWN, 1982).
6. N. Dunford and J. T. Schwartz, Linear Operators: Part I (Interscience, 1958).
7. W. Greenberg, C. Van der Mee and V. Protopopescu, Boundary Value Problems in Abstract Kinetic Theory (Birkhäuser, 1987).
8. M. A. Kirkilionis, O. Diekmann, B. Lisser, M. Nool, B. Sommeijer and A. M. De Roos, Numerical continuation of equilibria of physiologically structured population models. I. Theory, Math. Models Methods Appl. Sci. 11 (2001) 1101-1127.
9. M. A. Krasnosel'skii et al., Integral Operators in Space of Summable Functions (Noordhoff, 1976).
10. K. Latrach, On a nonlinear stationary problem arising in transport theory, J. Math. Phys. 37 (1996) 1336-1348.
11. K. Latrach, Compactness results for transport equations and applications, Math. Models Methods Appl. Sci. 11 (2001) 1181-1202.
12. K. Latrach and A. Jeribi, A nonlinear boundary value problem arising in growing cell populations, Nonlinear Anal. T.M.A. 36 (1999) 843-862.
13. M. Mokhtar-Kharroubi, Time asymptotic behaviour and compactness in neutron transport theory, Euro. J. Mech., B Fluid 11 (1992) 39-68.
14. M. Rotenberg, Transport theory for growing cell populations, J. Theor. Biol. 103 (1983) 181-199.
15. C. Van der Mee and P. Zweifel, A Fokker-Planck equation for growing cell populations, J. Math. Biol. 25 (1987) 61-72.
16. E. Zeidler, Nonlinear Functional Analysis and Its Applications I: Fixed-Point Theorems (Springer-Verlag, 1993).