On predator-prey dispersal, repulsive dispersal, and the presence of shock waves
Authors:
Michiel Bertsch and Morton E. Gurtin
Journal:
Quart. Appl. Math. 44 (1986), 339-351
MSC:
Primary 92A15; Secondary 35K57, 35L65
DOI:
https://doi.org/10.1090/qam/856189
MathSciNet review:
856189
Full-text PDF Free Access
References |
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Additional Information
- Robert A. Adams, Sobolev spaces, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1975. Pure and Applied Mathematics, Vol. 65. MR 0450957
G. I. Baranblatt, On certain nonstationary motions of liquids and gases in porous media, Prikl. Mat. Mekh. 16, 57–78 (1952)
- M. Bertsch, M. E. Gurtin, D. Hilhorst, and L. A. Peletier, On interacting populations that disperse to avoid crowding: preservation of segregation, J. Math. Biol. 23 (1985), no. 1, 1–13. MR 821681, DOI https://doi.org/10.1007/BF00276555
M. E. Gurtin, The linear theory of elasticity, Handbuch der Physik (C. Truesdell, ed.), vol. VIa/2, Springer-Verlag, Berlin (1972)
- Morton E. Gurtin and A. C. Pipkin, A note on interacting populations that disperse to avoid crowding, Quart. Appl. Math. 42 (1984), no. 1, 87–94. MR 736508, DOI https://doi.org/10.1090/S0033-569X-1984-0736508-X
- R. C. MacCamy, Simple population models with diffusion, Comput. Math. Appl. 9 (1983), no. 3, 341–344. Hyperbolic partial differential equations. MR 702652, DOI https://doi.org/10.1016/0898-1221%2883%2990021-4
- R. E. Pattle, Diffusion from an instantaneous point source with a concentration-dependent coefficient, Quart. J. Mech. Appl. Math. 12 (1959), 407–409. MR 114505, DOI https://doi.org/10.1093/qjmam/12.4.407
- Joel Smoller, Shock waves and reaction-diffusion equations, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 258, Springer-Verlag, New York-Berlin, 1983. MR 688146
R. A. Adams, Sobolev spaces, Academic Press, New York (1975)
G. I. Baranblatt, On certain nonstationary motions of liquids and gases in porous media, Prikl. Mat. Mekh. 16, 57–78 (1952)
M. Bertsch, M. E. Gurtin, D. Hilhorst and L. A. Peletier, On interacting populations that disperse to avoid crowding: preservation of segregation, J. Math. Biol. 23, 1–13 (1985)
M. E. Gurtin, The linear theory of elasticity, Handbuch der Physik (C. Truesdell, ed.), vol. VIa/2, Springer-Verlag, Berlin (1972)
M. E. Gurtin and A. C. Pipkin, A note on interacting populations that disperse to avoid crowding, Quart. Appl. Math. 42, 87–94 (1984)
R. C. MacCamy, Simple population models with diffusion, Comp. Math. Appl. 9, 341–344 (1982)
R. E. Pattle, Diffusion from an instantaneous point source with concentration-dependent coefficient, Quart. J. Mech. Appl. Math. 12, 407–409 (1959)
J. Smoller, Shock waves and reaction-diffusion equations, Springer-Verlag, Berlin (1983)
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Article copyright:
© Copyright 1986
American Mathematical Society