Skip to main content
SpringerLink
Log in

Perturbation Results for Multivalued Linear Operators

  • Chapter
  • First Online:
Book cover Parabolic Problems

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications ((PNLDE,volume 80))

Abstract

We give some perturbation theorems for multivalued linear operators in a Banach space. Two different approaches are suggested: the resolvent approach and the modified resolvent approach. The results allow us to handle degenerate abstract Cauchy problems (inclusions). A very wide application of obtained abstract results to initial boundary value problems for degenerate parabolic (elliptic-parabolic) equations with lower-order terms is studied. In particular, integro-differential equations have been considered too.

Mathematics Subject Classification (2000). Primary 47A06; 47A55; Secondary 35K65; 35K30; 35M13.

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
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. R. Cross, Multivalued Linear Operators, Marcel Dekker, Inc., 1998.

    Google Scholar 

  2. H.O. Fattorini, The Cauchy Problem, Encyclopedia of Mathematics and its Application, Addison Wesley, London, 1983.

    MATH  Google Scholar 

  3. A. Favaron and A. Lorenzi, Gradient estimates for solutions of parabolic differential equations degenerating at infinity, Advances Diff. Eqs., (4) 12 (2007), 435–460.

    MATH  MathSciNet  Google Scholar 

  4. A. Favini, A. Lorenzi, H. Tanabe, and A. Yagi, An L p -approach to singular linear parabolic equations in bounded domains, Osaka J. Math., 42 (2005), 385–406.

    MATH  MathSciNet  Google Scholar 

  5. A. Favini, A. Lorenzi, H. Tanabe, and A. Yagi, An L p -approach to singular linear parabolic equations with lower order terms, Discrete and Continuous Dynamical Systems, (4) 22 (2008), 989–1008.

    Article  MATH  MathSciNet  Google Scholar 

  6. A. Favini and A. Yagi, Degenerate Differential Equations in Banach Spaces, Marcel Dekker, Inc., New York, USA, 1999.

    MATH  Google Scholar 

  7. A. Favini and A. Yagi, Quasilinear degenerate evolution equations in Banach spaces, J. Evol. Eqs., 4 (2004), 421–449.

    Article  MATH  MathSciNet  Google Scholar 

  8. A. Favini and A. Yagi, Multivalued linear operators and degenerate evolution equations, Ann. Mat. Pura Appl., (4) 163 (1993), 353–384.

    Article  MATH  MathSciNet  Google Scholar 

  9. M. Haase, The Functional Calculus for Sectorial Operators, Birkhäuser Verlag, 2006.

    Google Scholar 

  10. A. Lunardi, Analytic Semigroups and Optimal Regularity in Parabolic Problems, Birkhäuser Verlag, Boston, 1995.

    MATH  Google Scholar 

  11. I.V. Melnikova and A. Filinkov, Abstract Cauchy Problems: Three Approaches, Chapman & Hall/CRC, Boca Raton, USA, 2001.

    Book  MATH  Google Scholar 

  12. S. Yakubov and Ya. Yakubov, Differential-Operator Equations. Ordinary and Partial Differential Equations, Chapman & Hall/CRC, Boca Raton, USA, 2000.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch, 7700, Cape Town, South Africa

    Ronald Cross

  2. Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato, 5, I-40126, Bologna, Italy

    Angelo Favini

  3. Raymond and Beverly Sackler School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv, 69978, Israel

    Yakov Yakubov

Authors
  1. Ronald Cross
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Angelo Favini
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yakov Yakubov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ronald Cross .

Editor information

Editors and Affiliations

  1. Inst. Angewandte Mathematik, Leibniz Universität Hannover, Welfengarten 1, Hannover, 30167, Germany

    Joachim Escher

  2. School of Physical Sciences, Dept. Mathematics, University of California, Irvine, Irvine, 92697-3875, California, USA

    Patrick Guidotti

  3. , Fachbereich Mathematik, TU Darmstadt, Schlossgartenstr 7, Darmstadt, 64289, Germany

    Matthias Hieber

  4. Inst. Applied Mathematics & Mechanics, Warsaw University, ul. Banacha 2, Warszawa, 02-097, Poland

    Piotr Mucha

  5. , FB Mathematik und Informatik, Universität Halle-Wittenberg, Theodor-Lieser-Strasse 5, Halle, 06099, Germany

    Jan W. Prüss

  6. 3-4-1, Ohkubo Shinjuku-ku, Tokyo, 169-8555, Japan

    Yoshihiro Shibata

  7. , Deparment of Mathematics, Vanderbilt University, 1326 Stevenson Center, Nashville, TN 37240, USA

    Gieri Simonett

  8. Inst. Angewandte Mathematik, Leibniz Universität Hannover, Welfengarten 1, Hannover, 30167, Germany

    Christoph Walker

  9. Fac. Mathematics & Information Sciences, Warsaw University of Technology, pl. Politechniki 1, Warszawa, 00-661, Poland

    Wojciech Zajaczkowski

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer Basel AG

About this chapter

Cite this chapter

Cross, R., Favini, A., Yakubov, Y. (2011). Perturbation Results for Multivalued Linear Operators. In: Escher, J., et al. Parabolic Problems. Progress in Nonlinear Differential Equations and Their Applications, vol 80. Springer, Basel. https://doi.org/10.1007/978-3-0348-0075-4_7

Download citation

Publish with us

Policies and ethics

Search

Navigation