Skip to main content
SpringerLink
Log in

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

  • Published:
Mathematische Zeitschrift Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Amann, H.: Quasilinear parabolic systems under nonlinear boundary conditions. Arch. Radional Mech. Anal.92, 153–192 (1986)

    Google Scholar 

  2. Friedman, A.: Partial differential equations of parabolic type. Englewood Cliffs, N.J.: Prentice Hall 1964

    Google Scholar 

  3. Gilbarg, D., Trudinger, N.S.: Elliptic partial differential equations of second order. Berlin Heidelberg New York: Springer 1977

    Google Scholar 

  4. Kawasaki, K., Shigesada, N., Teramoto, E.: Spatial segregation of interacting species. J. Theor. Biol.79, 83–99 (1979)

    Google Scholar 

  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. 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. Matano, H., Mimura, M.: Pattern formation in competition-diffusion systems in nonconvex domains. Publ. RIMS, Kyoto Univ.19, 1049–1979 (1983)

    Google Scholar 

  8. Mimura, M.: Stationary pattern of some density-dependent diffusion system with competitive dynamics. Hiroshima Math. J.11, 621–635 (1981)

    Google Scholar 

  9. Pogorzelski, W.: Propriétés des intégrales de l'équation parabolique normale. Ann. Pol. Mat.4, 61–92 (1957)

    Google Scholar 

  10. Smoller, J.: Shock waves and reaction-diffusion equations. Berlin Heidelberg New York: Springer 1983

    Google Scholar 

  11. Wahl, W. von: The equations of Navier-Stokes and abstract parabolic equations. Braunschweig: Vieweg 1985

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematisches Institut der Universität, D-8580, Bayreuth, Federal Republic of Germany

    Paul Deuring

Authors
  1. Paul Deuring
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Deuring, P. An initial-boundary-value problem for a certain density-dependent diffusion system. Math Z 194, 375–396 (1987). https://doi.org/10.1007/BF01162244

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01162244

Keywords

Search

Navigation