An analytical framework to describe the interactions between individuals and a continuum

Journal of Nonlinear Science

Volumn 22, Issue 1, 2012, Pages 39-61

  Colombo, Rinaldo M ^a   Lécureux Mercier, Magali ^b  

^a UNIVERSITY OF BRESCIA   (Italy)

^b UNIVERSITÉ D'ORLÉANS   (France)

Author keywords

Conservation laws; Mixed P.D.E. O.D.E. problems; Ordinary differential equations

Indexed keywords

CAUCHY PROBLEMS; CONSERVATION LAW; DISCRETE SETS; INDIVIDUAL AGENT; MIXED P.D.E.-O.D.E. PROBLEMS; NUMERICAL INTEGRATIONS; SCALAR CONSERVATION LAWS; SPACE DIMENSIONS; SYSTEM OF ORDINARY DIFFERENTIAL EQUATIONS; WELLPOSEDNESS;

PHYSICAL PROPERTIES;

ORDINARY DIFFERENTIAL EQUATIONS;

EID: 84856516182     PISSN: 09388974     EISSN: 14321467     Source Type: Journal    
DOI: 10.1007/s00332-011-9107-0     Document Type: Article

References (15)

1. Borsche, R., Colombo, R.M., Garavello, M.: On the coupling of systems of hyperbolic conservation laws with ordinary differential equations. Nonlinearity 23, 2749-2770 (2010)
2. Bressan, A., De Lellis, C.: Existence of optimal strategies for a fire confinement problem. Commun. Pure Appl. Math. 62(6), 789-830 (2009)
3. Capasso, V., Micheletti, A., Morale, D.: Stochastic geometric models, and related statistical issues in tumour-induced angiogenesis. Math. Biosci. 214(1-2), 20-31 (2008)
4. Colombo, R.M.,Mercier,M., Rosini,M.D.: Stability and total variation estimates on general scalar balance laws. Commun. Math. Sci. 7(1), 37-65 (2009)
5. Colombo, R.M., Herty, M., Mercier, M.: Control of the continuity equation with a non-local flow. ESAIM Control Optim. Calc. Var. 17, 353-379 (2011). doi:10.1051/cocv/2010007
6. Filippov, A.F.: Differential Equations with Discontinuous Righthand Sides. Kluwer Academic, Dordrecht (1988). Translated from the Russian
7. Grimm, J., Grimm, W.: Deutsche Sagen, 2nd edn. Nicolaische Verlagsbichhandlung, Berlin (1865)
8. Hoff, W.D., van der Horst, M.A., Nudel, C.B., Hellingwerf, K.J.: In: Prokaryotic Phototaxis, vol. 571, pp. 25-49. Springer, Berlin (2009). Chapter 2
9. Kružkov, S.N.: First order quasilinear equations with several independent variables. Mat. Sb. (N.S.) 81(123), 228-255 (1970)
10. Lattanzio, C., Maurizi, A., Piccoli, B.: Moving bottlenecks in car traffic flow: a pde-ode coupled model. Preprint (2010)
11. Lécureux-Mercier, M.: Improved stability estimates on general scalar balance laws. J. Hyperbolic Differ. Equ. (2011, to appear)
12. LeVeque, R.J.: Finite Volume Methods for Hyperbolic Problems Cambridge Texts in Applied Mathematics. Cambridge University Press, Cambridge (2002)
13. Serre, D.: Chute libre d'un solide dans un fluide visqueux incompressible. Existence. Jpn. J. Appl. Math. 4(1), 99-110 (1987)
14. Vázquez, J.L., Zuazua, E.: Large time behavior for a simplified 1D model of fluid-solid interaction. Commun. Partial Differ. Equ. 28(9-10), 1705-1738 (2003) (Pubitemid 37211640)
15. Witman, G.B.: Chlamydomonas phototaxis. Trends Cell Biol. 3(11), 403-408 (1993) (Pubitemid 23315054)