Diffusion-aggregation processes with mono-stable reaction terms

Discrete and Continuous Dynamical Systems - Series B

Volumn 6, Issue 5, 2006, Pages 1175-1189

  Maini, Philip K ^a   Malaguti, Luisa ^b   Marcelli, Cristina ^c   Matucci, Serena ^d  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b UNIVERSITY OF MODENA AND REGGIO EMILIA   (Italy)

^c UNIVERSITÀ POLITECNICA DELLE MARCHE   (Italy)

^d UNIVERSITY OF FLORENCE   (Italy)

Author keywords

Diffusion aggregation processes; Finite speed of propagation; Front propagation; Population dynamics; Sharp profiles

Indexed keywords

EID: 33748522369     PISSN: 15313492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (18)

1. W. Alt, Models for mutual attraction and aggregation of motile individuals, Mathematics in biology and medicine, Lecture Notes in Biomathematics, 57, Springer-Verlag, New York, (1985), 33-38.
2. D.G. Aronson, The role of diffusion in mathematical population biology: Skellam revisited, Mathematics in biology and medicine, Lecture Notes in Biomathematics, 57, Springer-Verlag, New York, (1985), 2-6.
3. D.G. Aronson and H.F. Weinberger, Multidimensional nonlinear diffusion arising in population genetics, Adv. Math., 30 (1978), 33-76.
4. P.C. Fife, Mathematical Aspects of Reacting and Diffusing Systems, Lecture Notes in Biomathematics, 28, Springer-Verlag, New York, 1979.
5. B.H. Gilding and R. Kersner, Travelling Waves in Nonlinear Diffusion-Convection-Reaction, Birkhäuser Verlag, Basel, 2004.
6. J. Hadamard, Lectures on Cauchy's problem in linear partial differential equations. Dover Publications, New York, 1953.
7. S. Kamin and P. Rosenau, Emergence of waves in a nonlinear convection-reaction-diffusion equation, Adv. Nonlinear Stud., 4 (2004), 251-272.
8. L. Malaguti and C. Marcelli. Travelling wavefronts in reaction-diffusion equations with convection effects and non-regular terms, Math. Nachr., 242 (2002), 1-17.
9. L. Malaguti and C. Marcelli, Sharp profiles in degenerate and doubly-degenerate Fisher-KPP equations, J. Diff. Eqs., 195 (2003), 471-496.
10. L. Malaguti and C. Marcelli, Finite speed of propagation in monostable degenerate reactiondiffusion-convection equations, Adv. Nonlinear Stud., 5 (2005), 223-252.
11. K. Muller Efficient numerical methods for backward solution of parabolic problems with variable coefficients, Improperly posed boundary value problems, A.Carasso and A.P. Stone eds., London, Pitman, (1975), 54-64.
12. J.D. Murray, Mathematical Biology, Springer-Verlag, Berlin, 2003.
13. V. Padrón, Effect of aggregation on population revovery modeled by a forward-backward pseudoparabolic equation, Trans. Amer. Math. Soc., 356 (2004), 2739-2756.
14. F. Sánchez-Garduño and P.K. Maini, Existence and uniqueness of a sharp travelling wave in degenerate non-linear diffusion Fisher-KPP equation, J. Math. Biol., 33 (1994), 163-192.
15. F. Sánchez-Garduño and P.K. Maini, Travelling wave phenomena in some degenerate reaction-diffusion equations, J. Diff. Eqs., 117 (1995), 281-319.
16. F. Sánchez-Garduño and P.K. Maini, A non-linear degenerate equation for direct aggregation, preprint.
17. R.A. Satnoinanu, P.K. Maini, F. Sánchez-Garduño and J.P. Armitage, Travelling waves in a nonlinear degenerate diffusion model for bacterial pattern formation, Discr. Cont. Dyn. Syst. Ser. B, 1 (2001), 339-362.
18. P. Turchin, Population consequences of aggregative movements, J. of Animal Ecol., 58 (1989), 75-100.