Skip to main content
SpringerLink
Log in

Nonexistence of Global Solutions of Higher Order Evolution Inequalities in RN

  • Conference paper
Nonlinear Equations: Methods, Models and Applications

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications ((PNLDE,volume 54))

Abstract

This paper is devoted to the study of the nonexistence of global nontrivial weak solutions of higher order evolution inequalities in RNof the form: where we assume that m andkare integers greater or equal to 1,q >1 anda <2m. The idea is to find a set of conditions which imply the nonexistence of global weak solutions and to see how this set depends on the order of the operator. In particular, we will define an exponentq*such that ifq < q*, then (1)—(2) does not admit any nontrivial solution in a weak sense to be specified later, (see Definition 2.1). We will address toq*as to thecritical exponentof problem (1)—(2)

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 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. C. Bandle,H. A. Levine,Q. Zhang, Critical exponents of Fujita type for inhomogeneous parabolic equations and systems, J. Math. Anal. Appl., 251 (2000), 624–648.

    Article  MathSciNet  MATH  Google Scholar 

  2. G. Caristi, Existence and nonexistence of global solutions of degenerate and singular parabolic systems, Abstract and Applied Analysis, 5 (2000), 265–284.

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  4. H. Fujita, On the blowing up of solutions of the Cauchy problem for J. Fac. Sci. Univ. Tokio Sec. lA Math. 16 (1966), 105–113.

    Google Scholar 

  5. J. Giacomoni, Some results about blow-up and global existence to a semilinear degenerate heat equation, Rev. Mat. Complut. 11 (1998), 325–351.

    MathSciNet  MATH  Google Scholar 

  6. M.O. Korpusov, Yu.D. Peletier, A.G. Sveshnikov, Unsteady waves in anisotropic dispersive media, Comput. Math. Math. Phys. 39 (1999), 968–984.

    MathSciNet  MATH  Google Scholar 

  7. G.G. Laptev, Some nonexistence results for higher order evolution inequalities in cone-like domains, Electronic Research Announcements of AMS, 7 (2001), 87–93.

    Article  MathSciNet  MATH  Google Scholar 

  8. H. Levine, The role of critical exponents in blow-up theorems, SIAM Reviews, 32 (1990), 262–288.

    Article  MATH  Google Scholar 

  9. E. Mitidieri, S.I. Pohozaev, Nonexistence of weak solutions for degenerate and singular hyperbolic problems on RNProc. Steklov Inst. Math., 232 (2000), 1–19.

    MathSciNet  Google Scholar 

  10. E. Mitidieri, S.I. Pohozaev, Nonexistence of weak solutions for some degenerate elliptic and parabolic problems on RNJ. Evolution Equations, 1 (2001), 189–220.

    Article  MathSciNet  MATH  Google Scholar 

  11. E. Mitidieri, S.I. Pohozaev, A priori estimates and nonexistence of solutions to nonlinear partial differential equations and inequalities, Proc. Steklov Inst. Math., 234, (2001).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Scienze Matematiche, Università di Trieste, I-34100, Trieste, Italy

    Gabriella Caristi

Authors
  1. Gabriella Caristi
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133, Milano, Italy

    Daniela Lupo  & Carlo D. Pagani  & 

  2. Dipartimento di Matematica, Università degli Studi di Milano, Via Saldini, 50, 20133, Milano, Italy

    Bernhard Ruf

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer Basel AG

About this paper

Cite this paper

Caristi, G. (2003). Nonexistence of Global Solutions of Higher Order Evolution Inequalities in RN . In: Lupo, D., Pagani, C.D., Ruf, B. (eds) Nonlinear Equations: Methods, Models and Applications. Progress in Nonlinear Differential Equations and Their Applications, vol 54. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8087-9_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-8087-9_7

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9434-0

  • Online ISBN: 978-3-0348-8087-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation