Skip to main content
Log in

Analytic solutions of some nonlinear diffusion equations

  • 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

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

Instant access to the full article PDF.

References

  1. Berger, M.S.: Nonlinearity and Functional Analysis. New York-San Francisco-London: Academic Press 1977

    Google Scholar 

  2. Dieudonne, J.: Foundations of Modern Analysis. New York-San Francisco-London: Academic Press 1967

    Google Scholar 

  3. Friedman, A.: Partial Differential Equations. New York-Chicago-London: Holt, Rinehart and Winston, Inc. 1967

    Google Scholar 

  4. Fujita, H.: On some nonexistence and nonuniqueness theorems for nonlinear parabolic equations. In: Proceedings of the Symposium on Pure Mathematics. Amer. Math. Soc.18, 105–113 (1970)

  5. Fujiwara, D.: Concrete characterization of the domain of the fractional powers of some elliptic operators of the second order. Proc. Japan Acad.43, 82–86 (1967)

    Google Scholar 

  6. Furuya, K.: Analyticity of solutions of quasilinear evolution equations. Osaka J. Math.18, 669–698 (1981)

    Google Scholar 

  7. Hayden, T., Massey III, F.: Nonlinear holomorphic semigroups. Pac. J. Math.57, 423–439 (1975)

    Google Scholar 

  8. Kato, T.: Perturbation Theory for Linear Operators. Berlin-Heidelberg-New York: Springer 1966

    Google Scholar 

  9. Kato, T.: Fractional powers of dissipative operators. J. Math. Soc. Japan13, 246–274 (1961)

    Google Scholar 

  10. Kato, T., Tanabe, H.: On the abstract evolution operators. Osaka Math. J.14, 107–133

  11. Masuda, K.: On the holomorphic evolution operators. J. Math. Anal. Appl.39, 706–711 (1972)

    Google Scholar 

  12. Masuda, K.: On the analyticity and the unique continuation theorems for solutions of the Navier-Stokes equations. Proc. Japan Acad.43, 827–832 (1967)

    Google Scholar 

  13. Masuda, K.: Blow-up of solutions of some nonlinear diffusion equations. To appear in: Proceedings of 1982 US-Japan Symposium on Nonlinear Partial Equations

  14. Pazy, A.: Semigroups of Linear Operators and Applications to Partial Differential Equations. Berlin-Heidelberg-New York: Springer 1983

    Google Scholar 

  15. Sobolevskii, P.E.: Parabolic equations in a Banach space with an unbounded variable operator, a fractional power of which has a constant domain of definition. Dokl. Akad. Nauk SSSR138, 59–62 (1961)

    Google Scholar 

  16. Tanabe, H.: Equations of Evolutions. London: Pitman 1979

    Google Scholar 

  17. Tsutsumi, M.: Existence and nonexistence of global solutions for nonlinear parabolic equations. Publ. RIMS, Kyoto Univ.8, 211–229 (1972/1973)

    Google Scholar 

  18. Weissler, F.B.: Local existence and nonexistence for semilinear equations inL p. Indiana Univ. J.29, 79–102 (1980)

    Google Scholar 

  19. Yosida, K.: Functional Analysis. the Second Edition. Berlin-Heidelberg-New York: Springer 1968

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Masuda, K. Analytic solutions of some nonlinear diffusion equations. Math Z 187, 61–73 (1984). https://doi.org/10.1007/BF01163166

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01163166

Keywords

Navigation