Skip to main content
SpringerLink
Log in
Book cover

Advances in Applied Mathematics pp 231–238Cite as

Blowup of Series Solutions on the Half Line

  • Conference paper
  • First Online:

  • 1348 Accesses

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 87))

Abstract

We prove the convergence of series solutions of a semilinear reaction diffusion equation on the half line with quadratic nonlinearity. We also construct a positive solution that blows up in finite time. The algorithm, which is based on algebraic operations only, is fast and can be used to approximate and extend these solutions beyond blowup.

This is a preview of subscription content, 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
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

Learn about institutional subscriptions

References

  1. Boumenir, A.: Power series solutions for the KPP equation. Numer. Algor. 43(2), 177–187 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  2. Friedman, A., Mcleod, J.B.: Blow-up of positive solutions of semilinear heat equations. Indiana Univ. Math. J. 34, 425–447 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  3. Fujita, H.: On the blowing up of solutions to the Cauchy problem J. Fac. Sci. Univ. Tokyo, Sect. IA, Math. 18, 109–124 (1966)

    Google Scholar 

  4. Galaktionov, V.A.: On new exact blow-up solutions for nonlinear heat conduction equations, with source and applications. Diff. Integr. Equat. 3, 863–874 (1990)

    MATH  MathSciNet  Google Scholar 

  5. Galaktionov, V.A., Vazquez, J.L.: Continuation of blowup solutions of nonlinear heat equations in several space dimensions. Comm. Pure Appl. Math. 50(1), 1–67 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  6. Galaktionov, V.A., Svirshchevskii, S.R.: Exact solutions and invariant subspaces of nonlinear partial differential equations in mechanics and physics. Chapman Hall/CRC Applied Mathematics and Nonlinear Science Series. Chapman Hall/CRC, Boca Raton, FL (2007)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Kuwait University, Kuwait, Kuwait

    A. Boumenir

Authors
  1. A. Boumenir
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Boumenir .

Editor information

Ali R. Ansari

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Boumenir, A. (2014). Blowup of Series Solutions on the Half Line. In: Ansari, A. (eds) Advances in Applied Mathematics. Springer Proceedings in Mathematics & Statistics, vol 87. Springer, Cham. https://doi.org/10.1007/978-3-319-06923-4_22

Download citation

Publish with us

Policies and ethics

Search

Navigation