Diffusion and bifurcation problems in singularly perturbed domains

Natural Resource Modeling

Volumn 13, Issue 2, 2000, Pages 271-302

  Ward, Michael J ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 35348927313     PISSN: 08908575     EISSN: 19397445     Source Type: Journal    
DOI: 10.1111/j.1939-7445.2000.tb00036.x     Document Type: Article

References (14)

1. H.S. Carslaw and J.C. Jaeger [1959], Conduction of Heat in Solids, Clarendon Press, Oxford.
2. J. Crank [1983], The Mathematics of Diffusion, Oxford Science Publications, Clarendon Press, Oxford.
3. M.K. Holmes [1995], Introduction to Perturbation Methods, Springer-Verlag, New York.
4. A.M. Il'in [1992], Matching of Asymptotic Expansions of Solutions of Boundary Value Problems, Amer. Math. Soc., Providence, RI.
5. J.D. Jackson [1975], Classical Electrodynamics, 2nd ed., John Wiley and Sons, New York.
6. J. Kevorkian and J. Cole [1996], Multiple Scale and Singular Perturbation Methods, Appl. Math. Sci. 114, Springer, New York.
7. C. Lange and H. Weinitschke [1994], Singular Perturbations of Elliptic Problems on Domains with Small Holes, Studies Appl. Math. 92, 55–93.
8. D. Ludwig, D.G. Aronson and H.F. Weinberger [1979], Spatial Patterning of the Spruce Budworm, J. Math. Biology 8, 217–258.
9. J.D. Murray [1989], Mathematical Biology, Biomathematics 19, Springer, New York.
10. S. Ozawa [1981], Singular Variation of Domains and Eigenvalues of the Lapla-cian, Duke Math. J. 48, 767–778.
11. S. Ozawa [1983], An Asymptotic Formula for the Eigenvalues of the Laplacian in a Three-Dimensional Domain with a Small Hole, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 30, 243–257.
12. T. Ranford [1995], Potential Theory in the Complex Plane, London Math. Soc. Stud. Texts, 28, Cambridge University Press, Cambridge.
13. I. Sneddon [1951], Fourier Transforms, McGraw Hill, New York.
14. M.J. Ward, W.D. Henshaw and J.B. Keller [1993], Summing Logarithmic Expansions for Singularly Perturbed Eigenvalue Problems, SIAM J. Appl. Math. 53, 799–828.