Mathematische Zeitschrift

, Volume 194, Issue 3, pp 375–396 | Cite as

An initial-boundary-value problem for a certain density-dependent diffusion system

  • Paul Deuring
Article

Keywords

Diffusion System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Amann, H.: Quasilinear parabolic systems under nonlinear boundary conditions. Arch. Radional Mech. Anal.92, 153–192 (1986)Google Scholar
  2. 2.
    Friedman, A.: Partial differential equations of parabolic type. Englewood Cliffs, N.J.: Prentice Hall 1964Google Scholar
  3. 3.
    Gilbarg, D., Trudinger, N.S.: Elliptic partial differential equations of second order. Berlin Heidelberg New York: Springer 1977Google Scholar
  4. 4.
    Kawasaki, K., Shigesada, N., Teramoto, E.: Spatial segregation of interacting species. J. Theor. Biol.79, 83–99 (1979)Google Scholar
  5. 5.
    Kim Jong Uhn: Smooth solutions to a quasilinear system of diffusion equations for a certain population model. Nonlinear Anal.8, 1121–1144 (1984)Google Scholar
  6. 6.
    Ladyzenskaja, O.A., Ural'ceva, N.N., Solonnikov, V.A.: Linear and quasilinear equations of parabolic type. Am. Math. Soc.: Providence, R.I. Translations of Mathematical Monographs23 (1968)Google Scholar
  7. 7.
    Matano, H., Mimura, M.: Pattern formation in competition-diffusion systems in nonconvex domains. Publ. RIMS, Kyoto Univ.19, 1049–1979 (1983)Google Scholar
  8. 8.
    Mimura, M.: Stationary pattern of some density-dependent diffusion system with competitive dynamics. Hiroshima Math. J.11, 621–635 (1981)Google Scholar
  9. 9.
    Pogorzelski, W.: Propriétés des intégrales de l'équation parabolique normale. Ann. Pol. Mat.4, 61–92 (1957)Google Scholar
  10. 10.
    Smoller, J.: Shock waves and reaction-diffusion equations. Berlin Heidelberg New York: Springer 1983Google Scholar
  11. 11.
    Wahl, W. von: The equations of Navier-Stokes and abstract parabolic equations. Braunschweig: Vieweg 1985Google Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Paul Deuring
    • 1
  1. 1.Mathematisches Institut der UniversitätBayreuthFederal Republic of Germany

Personalised recommendations