Skip to main content
SpringerLink
Log in

On the Cauchy problem for a doubly nonlinear degenerate parabolic equation with strongly nonlinear sources

  • Published:
Science in China Series A: Mathematics Aims and scope Submit manuscript

Abstract

In this article, we consider the existence of local and global solution to the Cauchy problem of a doubly nonlinear equation. By introducing the norms |||f||| h and 〈f〉h, we give the sufficient and necessary conditions on the initial value to the existence of local solution of doubly nonlinear equation. Moreover some results on the global existence and nonexistence of solutions are considered.

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

Similar content being viewed by others

References

  1. Kalashnikov A S. Some problems of nonlinear parabolic equations of second order. Uspekhl Mat Nauk, 42(2): 169–222 (1987)

    MATH  MathSciNet  Google Scholar 

  2. Ladyzenskaya O A. New equations for the description of incompressible fluids and solvability in the large boundary value problem for them. Proc Steklov Inst Math, 102: 95–118 (1967)

    Google Scholar 

  3. Andreuccti D, Dibenedetto E. On the Cauchy problem and initial traces for a class of evolution equations with strongly nonlinear sources. Ann Sc Norm Super Pisacl Sci Ser IV Fasc, 3: 393–441 (1991)

    Google Scholar 

  4. Zhao J N. On the Cauchy problem and initial traces for evolution p-Laplacian equations with strongly nonlinear sources. J Differential Equations, 121: 329–383 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  5. Li J. Cauchy problem and initial traces for a doubly degenerate parabolic equation with strongly nonlinear sources. J Math Anal Appl, 264: 49–67 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  6. Ivanov A V. Hölder estimates quasilinear doubly degenerate parabolic equations. J Soviet Math, 56(12): 135–176 (1987)

    Google Scholar 

  7. Giaquinta M. Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. Princeton, NJ: Princeton University Press, 1983

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, China

    TingTing Zheng & JunNing Zhao

Authors
  1. TingTing Zheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. JunNing Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to TingTing Zheng.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant No. 10531020)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zheng, T., Zhao, J. On the Cauchy problem for a doubly nonlinear degenerate parabolic equation with strongly nonlinear sources. Sci. China Ser. A-Math. 51, 2059–2071 (2008). https://doi.org/10.1007/s11425-007-0168-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11425-007-0168-3

Keywords

MSC(2000)

Search

Navigation