Skip to main content
SpringerLink
Log in

Properties of Solutions of the Cauchy Problem for Degenerate Nonlinear Cross Systems with Convective Transfer and Absorption

  • Conference paper
  • First Online:
Algebra, Complex Analysis, and Pluripotential Theory (USUZCAMP 2017)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 264))

Included in the following conference series:

Abstract

In this paper the Cauchy problem for nonlinear systems is considered. The conditions of existence of the solutions on time for the problem Cauchy are given. Moreover the properties of the finite velocity of a propagation and localization of the disturbance, an asymptotic of self-similar solutions will be defined. The results of numerical solutions will be carried out and on the basis of calculations some necessary statements will be given.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Aripov, M.: Asymptotic of the solutions of the non-Newton polytrophic filtration equation. ZAMM 80(3), 767–768 (2000)

    Google Scholar 

  2. Aripov, M.: One invariant group method for the quasilinear equations and their system. In: Proceedings of the International Conference on Mathematics and its Applications in the New Millennium. Malaysia, pp. 535–543 (2000)

    Google Scholar 

  3. Aripov, M., Muhammadiev, J.: Asymptotic behavior of auto model solutions for one system of quasilinear equations of parabolic type. Buletin Stiintific-Universitatea din Pitesti, Seria Matematica si Informatica. 3, 19–40 (1999)

    Google Scholar 

  4. Aripov, M., Sadullaeva, ShA: An asymptotic analysis of a self-similar solution for the double nonlinear reaction-diffusion system. J. Nanosyst. Phys. Chem. Math. 6(6), 793–802 (2015)

    Article  Google Scholar 

  5. Aripov, M., Sadullaeva, ShA: Qualitative properties of solutions of a doubly nonlinear reaction-diffusion system with a source. J. Appl. Math. Phys. 3, 1090–1099 (2015)

    Article  Google Scholar 

  6. Cho, Chien-Hong: On the computation of the numerical blow-up time. Jpn. J. Ind. Appl. Math. 30(2), 331–349 (2013)

    Article  MathSciNet  Google Scholar 

  7. Deng, K., Levine, H.A.: The role of critical exponents in blow-up theorems: The sequel. J. Math. Anal. Appl. 243, 85–126 (2000)

    Article  MathSciNet  Google Scholar 

  8. Ferreira, Rael, Perez-Llanos, Mayte: Blow-up for the non-local -Laplacian equation with a reaction term. Nonlinear Anal.: Theory Methods Appl. 75(14), 5499–5522 (2012)

    Article  MathSciNet  Google Scholar 

  9. Jiang, Z.X., Zheng, S.N.: Doubly degenerate parabolic equation with nonlinear inner sources or boundary flux. Doctor Thesis, Dalian University of Technology, In China, (2009)

    Google Scholar 

  10. Martynenko, A.V., Tedeev, A.F.: The Cauchy problem for a quasilinear parabolic equation with a source and inhomogeneous density. Comput. Math. Math. Phys. 47(2), 238–248 (2007)

    Article  MathSciNet  Google Scholar 

  11. Martynenko, A.V., Tedeev, A.F.: On the behavior of solutions to the Cauchy problem for a degenerate parabolic equation with inhomogeneous density and a source. Comput. Math. Math. Phys. 48(7), 1145–1160 (2008)

    Article  MathSciNet  Google Scholar 

  12. Mu, C., Zheng, P.: Dengming Liu, Localization of solutions to a doubly degenerate parabolic equation with a strongly nonlinear source. Commun. Contemp. Math. 14, 1250018 [18 pages]. https://doi.org/10.1142/S0219199712500186

    Article  MathSciNet  Google Scholar 

  13. Sadullaeva, ShA: Numerical investigation of solutions to a reaction-diffusion system with variable density. Journal Sib. Fed. Univ. Math. Phys., J. Sib. Fed. Univ. Math. Phys. 9(1), 90–101 (2016)

    Article  MathSciNet  Google Scholar 

  14. Samarskii, A.A., Galaktionov, V.A., Kurduomov, S.P., Mikhailov, A.P.: Blowe-up in quasilinear parabolic equations, vol. 4, p. 535. Walter de Grueter, Berlin (1995)

    Book  Google Scholar 

  15. Tedeyev, A.F.: Conditions for the existence and nonexistence of a compact support in time of solutions of the Cauchy problem for quasilinear degenerate parabolic equations. Sib. Math. Jour. 45(1), 189–200 (2004)

    Google Scholar 

  16. Vazquez, J.L.: The Porous Medium Equation. Mathematical Theory, Oxford Mathematical Monographs, p. 430. The Clarendon Press, Oxford University Press, Oxford (2007)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Tashkent University of Information Technologies, TUIT, Tashkent, Uzbekistan

    Sh. A. Sadullaeva & M. B. Khojimurodova

Authors
  1. Sh. A. Sadullaeva
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. B. Khojimurodova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sh. A. Sadullaeva .

Editor information

Editors and Affiliations

  1. Department of Mathematics, California State University, Fullerton, CA, USA

    Zair Ibragimov

  2. Department of Mathematics, Indiana University, Bloomington, IN, USA

    Norman Levenberg

  3. Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan

    Utkir Rozikov

  4. Department of Mathematics, National University of Uzbekistan, Tashkent, Uzbekistan

    Azimbay Sadullaev

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Sadullaeva, S.A., Khojimurodova, M.B. (2018). Properties of Solutions of the Cauchy Problem for Degenerate Nonlinear Cross Systems with Convective Transfer and Absorption. In: Ibragimov, Z., Levenberg, N., Rozikov, U., Sadullaev, A. (eds) Algebra, Complex Analysis, and Pluripotential Theory. USUZCAMP 2017. Springer Proceedings in Mathematics & Statistics, vol 264. Springer, Cham. https://doi.org/10.1007/978-3-030-01144-4_15

Download citation

Publish with us

Policies and ethics

Search

Navigation