Skip to main content

Monotonicity and free boundary value problems

Part of the Lecture Notes in Mathematics book series (LNM,volume 773)

Abstract

Free boundary value problems were treated extensively in the last years, mostly by the help of discretization methods; here monotonicity properties are used, which give (in not too complicated cases) inclusion theorems for the free boundaries. This is illustrated in some examples, even in free boundary value problems in more dimensions.

Keywords

  • Free Boundary
  • Monotonicity Property
  • Free Boundary Problem
  • Stefan Problem
  • Move Boundary Problem

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   29.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   39.99
Price excludes VAT (Canada)
  • Compact, lightweight 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Baiocchi, C. Su un problema a frontiera libera connesso a questioni di idranlica; Ann. Pura Appl. (4) 92 (1972) 107–127

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. Bredendiek, E. Simultan Approximation, Arch.Rat.Mech.Anal. 33 (1969), 307–330.

    CrossRef  MathSciNet  Google Scholar 

  3. Bredendiek, E.-L. Collatz Simultan Approximation bei Randwertaufgaben, Internat. Ser. Num. Math. 30 (1976), 147–174

    MathSciNet  MATH  Google Scholar 

  4. Collatz, L. Aufgaben monotoner Art, Arch.Math.Anal.Mech. 3 (1952) 366–376

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. Collatz, L. The numerical treatment of some singular boundary value problems, Lect. Notes in Math. vol. 630, Springer 1978, 41–50

    Google Scholar 

  6. Collatz, L.-W. Wetterling Optimization problems, Springer 1975, 356 p.

    Google Scholar 

  7. Collatz, L.-H. Günther-J. Sprekels Vergleich zwischen Diskretisierungsverfahen und parametrischen Methoden an einfachen Testbeispielen, Z. Angew. Math. Mech., 56 (1976), 1–11

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. Crank, J.-R.S. Gupta Int. J. Heat Mass Transfer 18 (1975) 1101–1107

    CrossRef  Google Scholar 

  9. Hoffmann, K.H. Monotonie bei nichtlinearen Stefan Problemen Internat. Ser.Num.Math. vol. 39 (1978) 162–190

    MATH  Google Scholar 

  10. Friedman, A.-D. Kinderlehrer A one phase Stefan problem, Indiana U. Math. J., vol 24 (1975), 1005–1035

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. Meyn, K.H.-B. Werner Macimum and Monotonicity Principles for elliptic boundary value problems in partioned domains, to appear

    Google Scholar 

  12. Miller, J.V.-K.W. Morton-M.J. Baines A finite Element Moving Boundary Computation with an Adaptive Mesh, I. Inst. Maths Applies (1978) 22, 467–477

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. Ockendon, J.R. Numerical and Analytic Solutions of Moving Boundary Problems, (In the book of Wilson a.o., see below, p. 129–145.

    Google Scholar 

  14. Rubinstein, L.I. The Stefan Problem, Translat. Math. Monographs vol. 27, Amer. Math. Soc. 1971

    Google Scholar 

  15. Wilson, D.G.-A.D. Solomon-P.T. Boggs Moving Boundary Problems Acad. Press 1978, 329 p.

    Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1980 Springer-Verlag

About this paper

Cite this paper

Collatz, L. (1980). Monotonicity and free boundary value problems. In: Watson, G.A. (eds) Numerical Analysis. Lecture Notes in Mathematics, vol 773. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0094162

Download citation

  • DOI: https://doi.org/10.1007/BFb0094162

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09740-2

  • Online ISBN: 978-3-540-38562-2

  • eBook Packages: Springer Book Archive