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Monotone iterations for nonlinear obstacle problem

Published online by Cambridge University Press:  17 February 2009

Philip Korman ,
Anthony W. Leung  and
Srdjan Stojanovic
Philip Korman
Affiliation:
Department of Mathematical Sciences, University of Cincinnati, Cincinnati, Ohio 45221–0025, U.S.A.
Anthony W. Leung
Affiliation:
Department of Mathematical Sciences, University of Cincinnati, Cincinnati, Ohio 45221–0025, U.S.A.
Srdjan Stojanovic
Affiliation:
Department of Mathematical Sciences, University of Cincinnati, Cincinnati, Ohio 45221–0025, U.S.A.
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Abstract

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The existence, uniqueness and regularity of solutions are proved for the obstacle problem with semilinear elliptic partial differential equations of second order. Computationally effective algorithms are provided and application made to steady state problem for the logistic population model with diffusion and an obstacle to growth.

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 31 , Issue 3 , January 1990 , pp. 259 - 276
Copyright
Copyright © Australian Mathematical Society 1990

References

[1] Agmon, S., Douglis, A. and Nirenberg, L., “Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions”, I, Comm. Pure Appl. Math. 12 (1959) 623–727.CrossRefGoogle Scholar
[2] Amann, H., “Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces”, SIAM Rev. 18 (1976) 620–709.CrossRefGoogle Scholar
[3] Boccardo, L and Giachetti, D., “Strongly nonlinear unilateral problems”, Appl. Math. Optimaization 9 (1983) 291–301.CrossRefGoogle Scholar
[4] Brezis, H. and Browder, F. E., “Strongly nonlinear elliptic boundary value problems”, Annali Scuola Norm. Sup. Pisa (1978) 587–603.Google Scholar
[5] Caffarelli, L. A., “The regularity of free boundaries in higher dimension, Acta Math.”, 139 (1977) 155–184.Google Scholar
[6] Friedman, A., Variational principles and free-boundary problems (John Wiley and Sons, New York, 1982).Google Scholar
[7] Gilbarg, D. and Trudinger, N. S., Elliptic partial differential equations of second order (Springer-Verlag, New York, 1977).CrossRefGoogle Scholar
[8] Glowinski, R., Lectures on numerical methods for non-linear variational problems (TATA Institutie, Bombay, 1980).Google Scholar
[9] Keller, H. B., “Some positone problems suggested by nonlinear heat generation”, in Bifurcation theory and nonlinear eigenvalue problems, Keller, J. B. and Antman, S. Eds., (Benjamin, New York, 1969).Google Scholar
[10] Kinderlehrer, D. and Nirenberg, L., “Regularity in free boundary problems”, Ann. Scu. Norm. Sup. Pisa 4 (4) (1977) 373–391.Google Scholar
[11] Leung, A., “Monotone schemes for semilinear elliptic systems related to ecology”, Math. in Appl. Sci. 4 (1982) 272–285.Google Scholar
[12] Leung, A. W. and Murio, D. A., “Accelerated monotone scheme for finite difference equations concerning steady-state prey-predator interactions”, J. of Comput. and Appl. Math. 16 (1986) 333–341.CrossRefGoogle Scholar