Niveau: Supérieur, Doctorat, Bac+8
DISCRETE AND CONTINUOUS doi:10.3934/dcdsb.2009.12.xx DYNAMICAL SYSTEMS SERIES B Volume 12, Number 1, July 2009 pp. 1–XX STABILITY OF CONSTANT STATES AND QUALITATIVE BEHAVIOR OF SOLUTIONS TO A ONE DIMENSIONAL HYPERBOLIC MODEL OF CHEMOTAXIS Francesca Romana Guarguaglini Dipartimento di Matematica Pura e Applicata Universita degli Studi di L'Aquila Via Vetoio, I–67100 Coppito (L'Aquila), Italy Corrado Mascia Dipartimento di Matematica “G. Castelnuovo” Universita di Roma “La Sapienza” Piazzale A. Moro, 2, I–00185 Roma, Italy Roberto Natalini Istituto per le Applicazioni del Calcolo “Mauro Picone” Consiglio Nazionale delle Ricerche c/o Department of Mathematics, University of Rome “Tor Vergata” Via della Ricerca Scientifica, 1; I-00133 Roma, Italy Magali Ribot Laboratoire J. A. Dieudonne Universite de Nice-Sophia Antipolis Parc Valrose, F-06108 Nice Cedex 02, France (Communicated by Benoit Perthame) Abstract. We consider a general model of chemotaxis with finite speed of propagation in one space dimension. For this model we establish a general result of stability of some constant states both for the Cauchy problem on the whole real line and for the Neumann problem on a bounded interval. These results are obtained using the linearized operators and the accurate analysis of their nonlinear perturbations. Numerical schemes are proposed to approximate these equations, and the expected qualitative behavior for large times is compared to several numerical tests.
- state u±
- constant solutions
- general framework
- functions u±
- such kind
- system
- all stationary constant
- hyperbolic model
- model describing