References
Aronson, D. G., Peletier, L. A.: Large time behavior of solutions of the porous media equation. J. Differ. Equations 39, 378–412 (1981)
Bertsch, M., Hilhorst, D.: A density dependent diffusion equation in population dynamics: stabilization to equilibrium. To appear in SIAM J. Math. Anal.
Bertsch, M., Gurtin, M. E., Hilhorst, D., Peletier, L. A.: On interacting populations that disperse to avoid crowding: The effect of a sedentary colony. J. Math. Biol. 19 1–12 (1984)
Bertsch, M., Gurtin, M. E., Hilhorst, D.: The equation c(z) t=ϕ(z x)x: the free boundary induced by a discontinuity in the derivative of c. To appear
Busenberg, S. N., Travis, C. C.: Epidemic models with spatial spread due to population migration. J. Math. Biol. 16, 181–198 (1983)
Gurney, W. S. C., Nisbet, R. M.: The regulation of inhomogeneous populations. J. Theor. Biol. 52, 441–457 (1975)
Gurtin, M. E., MacCamy, R. C.: On the diffusion of biological populations. Math. Biosci. 33, 35–49 (1977)
Gurtin, M. E., Pipkin, A. C.: A note on interacting populations that disperse to avoid crowding. Q. Appl. Math. 42, 87–94 (1984)
Peletier, L. A.: The porpus media equation. Application of nonlinear analysis in the physical sciences, pp. 229–241. Amann, H., Bazley, N., Kirchgässner, K., (eds.) Boston: Pitman 1981
Shigesada, N., Kawasaki, K., Teramoto, E.: Spatial segregation of interacting species. J. Theor. Biol. 79, 83–99 (1979)
Bertsch, M., Gurtin, M. E.: On predator prey dispersal, repulsive dispersal and the presence of shock waves. To appear in Q. App. Math.
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Bertsch, M., Gurtin, M.E., Hilhorst, D. et al. On interacting populations that disperse to avoid crowding: preservation of segregation. J. Math. Biology 23, 1–13 (1985). https://doi.org/10.1007/BF00276555
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DOI: https://doi.org/10.1007/BF00276555