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Monotonicity and free boundary value problems

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Book cover Numerical Analysis

Part of the book series: Lecture Notes in Mathematics ((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.

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References

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  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

    Article  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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  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

    Article  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

    Article  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 

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Authors

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G. Alistair Watson

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© 1980 Springer-Verlag

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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

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

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09740-2

  • Online ISBN: 978-3-540-38562-2

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