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
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Baiocchi, C. Su un problema a frontiera libera connesso a questioni di idranlica; Ann. Pura Appl. (4) 92 (1972) 107–127
Bredendiek, E. Simultan Approximation, Arch.Rat.Mech.Anal. 33 (1969), 307–330.
Bredendiek, E.-L. Collatz Simultan Approximation bei Randwertaufgaben, Internat. Ser. Num. Math. 30 (1976), 147–174
Collatz, L. Aufgaben monotoner Art, Arch.Math.Anal.Mech. 3 (1952) 366–376
Collatz, L. The numerical treatment of some singular boundary value problems, Lect. Notes in Math. vol. 630, Springer 1978, 41–50
Collatz, L.-W. Wetterling Optimization problems, Springer 1975, 356 p.
Collatz, L.-H. Günther-J. Sprekels Vergleich zwischen Diskretisierungsverfahen und parametrischen Methoden an einfachen Testbeispielen, Z. Angew. Math. Mech., 56 (1976), 1–11
Crank, J.-R.S. Gupta Int. J. Heat Mass Transfer 18 (1975) 1101–1107
Hoffmann, K.H. Monotonie bei nichtlinearen Stefan Problemen Internat. Ser.Num.Math. vol. 39 (1978) 162–190
Friedman, A.-D. Kinderlehrer A one phase Stefan problem, Indiana U. Math. J., vol 24 (1975), 1005–1035
Meyn, K.H.-B. Werner Macimum and Monotonicity Principles for elliptic boundary value problems in partioned domains, to appear
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
Ockendon, J.R. Numerical and Analytic Solutions of Moving Boundary Problems, (In the book of Wilson a.o., see below, p. 129–145.
Rubinstein, L.I. The Stefan Problem, Translat. Math. Monographs vol. 27, Amer. Math. Soc. 1971
Wilson, D.G.-A.D. Solomon-P.T. Boggs Moving Boundary Problems Acad. Press 1978, 329 p.
Editor information
Editors and Affiliations
Rights 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
