Reaction transport equations in biological modeling

Mathematical and Computer Modelling

Volumn 31, Issue 4-5, 2000, Pages 75-81

  Hadeler, K P ^a  

^a UNIVERSITY OF TÜBINGEN   (Germany)

Author keywords

Boltzmann type equations; Evolution of density; Moving particles; Reaction law; Reaction transport equation

Indexed keywords

EID: 0034143283     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0895-7177(00)00024-8     Document Type: Conference Paper

References (24)

1. C. Cercignani, R. Illner and M. Pulvirenti, The Mathematical Theory of Dilute Gases, Springer-Verlag, (1994).
2. W. Alt, Biased random walk models for chemotaxis and related diffusion approximations, J. Math. Biol. 9, 147-177 (1980).
3. H.G. Othmer, S.R. Dunbar and W. Alt, Models of dispersal in biological systems, J. Math. Biol. 26, 263-298 (1988).
4. K.P. Hadeler, Travelling fronts for correlated random walks, Can. Appl. Math. Quart. 2, 27-43 (1994).
5. T. Hillen, Qualitative Analysis of Hyperbolic Random Walk Systems, Preprint, University of Tübingen, SFB 382, Report No. 43, (1995).
6. K.P. Hadeler, Reaction telegraph equations and random walk systems, In Stochastic and Spatial Structures of Dynamical Systems, (Edited by S.J. van Strien and S.M. Verduyn Lunal), Kon. Nederlandse Akad. Wetensch. Verhandl., Afd. Natuurkunde, 1 Serie, pp. 133-161, North-Holland, (1996).
7. H. Schwetlick, Reaction Transport Equations, Dissertation, Tübingen, (1997).
8. S. Goldstein, On diffusion by discontinuous movements and the telegraph equation, Quart. J. Mech. Appl. Math. 4, 129-156 (1951).
9. M. Kac, A stochastic model related to the telegrapher's equation, (1956); reprinted in Rocky Mtn. Math. J. 4, 497-509 (1974).
10. C. Cattaneo, Sulla conduzione del calore, Atti del Semin. Mat. E Fis., Univ. Modena 3, 83-101 (1948).
11. D.D. Joseph and L. Preziosi, Heat waves, Reviews of Modern Physics 61, 41-73 (1988).
12. K.P. Hadeler, Travelling fronts in random walk systems, Forma (Tokyo) 10, 223-233 (1995).
13. Th. Gallay and G. Raugel, Stability of travelling waves for a damped hyperbolic equation, J. Diff. Equ. 150, 42-97 (1998).
14. H. Schwetlick, On the Minimal Wave Speed for Reaction Transport Equations in Dimensions N ≥ 2. Preprint, University of Tübingen, SFB 382, Report No. 73, (1997).
15. A. Källén, Thresholds and travelling waves in an epidemic model for rabies, Nonlinear Analysis TMA 8, 851-856 (1984).
16. K.P. Hadeler, Travelling epidemic waves and correlated random walks, In Differential Equations and Applications to Biology and to Industry, (Edited by M. Martelli et al.), pp. 145-156, World Scientific, (1996).
17. K.P. Hadeler, Spatial epidemic spread, with slow infectives, In Ordinary and Partial Differential Equations, Proc. Conf. Dundee, 1996, (Edited by R.J. Jarvis et al.), pp. 18-32, Pitman Research Notes, Math. Series 370, (1997).
18. T. Hillen, A Turing model with correlated random walk, J. Math. Biol. 35, 49-72 (1996).
19. T. Hillen, Nonlinear hyperbolic systems describing random motion and their application on the Turing model, Dissertation Summarizes 1, 121-128 (1996).
20. T. Hillen, Qualitative analysis of Cattaneo systems, Preprint, University of Tübingen, SFB 382, Report No. 59, (1997); Math. Models and Methods in Applied Sciences 3 (8) (to appear).
21. T. Hillen, Invariance principles for hyperbolic random walk systems, J. Math. Anal. Appl. 210, 360-374 (1997).
22. K.P. Hadeler, Reaction-telegraph equations with density-dependent coefficients, In Part. Diff. Equ., Models in Physics and Biology, Mathematical Research, Vol. 82, (Edited by G. Lumer et al.), pp. 152-158, Akademie-Verlag, Berlin, (1994).
23. K.P. Hadeler, Reaction transport systems in biological modelling, In CIME Lectures 1997, Mathematics Inspired by Biology, (Edited by V. Capasso and O. Diekmann), Springer-Verlag, Florence, (1999).
24. K.P. Hadeler, Nonlinear propagation in reaction transport systems, Fields Institute Communications 21, 251-257 (1999).