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DOMAIN PERTURBATION FOR PARABOLIC EQUATIONS

Published online by Cambridge University Press:  16 December 2011

PARINYA SA NGIAMSUNTHORN*
Affiliation:
School of Mathematics and Statistics, University of Sydney, NSW, 2006, Australia (email: [email protected])
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Abstract

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Type
Research Article
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

References

[1]Arendt, W., ‘Approximation of degenerate semigroups’, Taiwanese J. Math. 5(2) (2001), 279295.CrossRefGoogle Scholar
[2]Bucur, D. and Varchon, N., ‘Boundary variation for a Neumann problem’, Ann. Sc. Norm. Super. Pisa Cl. Sci. 29(4) (2000), 807821.Google Scholar
[3]Dancer, E. N., ‘The effect of domain shape on the number of positive solutions of certain nonlinear equations’, J. Differential Equations 74(1) (1988), 120156.CrossRefGoogle Scholar
[4]Dancer, E. N., ‘The effect of domain shape on the number of positive solutions of certain nonlinear equations. II’, J. Differential Equations 87(2) (1990), 316339.CrossRefGoogle Scholar
[5]Daners, D., ‘Domain perturbation for linear and nonlinear parabolic equations’, J. Differential Equations 129(2) (1996), 358402.CrossRefGoogle Scholar
[6]Daners, D., ‘Dirichlet problems on varying domains’, J. Differential Equations 188(2) (2003), 591624.CrossRefGoogle Scholar
[7]Daners, D., ‘Perturbation of semi-linear evolution equations under weak assumptions at initial time’, J. Differential Equations 210(2) (2005), 352382.CrossRefGoogle Scholar
[8]Daners, D., ‘Domain perturbation for linear and semi-linear boundary value problems’, in: Handbook of Differential Equations: Stationary Partial Differential Equations, Vol. 6 (ed. Chipot, M.) (Elsevier, North Holland, Amsterdam, 2008), pp. 181.Google Scholar
[9]Mosco, U., ‘Convergence of convex sets and of solutions of variational inequalities’, Adv. Math. 3 (1969), 510585.CrossRefGoogle Scholar
[10]Sa Ngiamsunthorn, P., ‘Persistence of bounded solutions of parabolic equations under domain perturbation’, J. Evol. Equ., in press, doi 10.1007/s00028–011–0121–3.Google Scholar
[11]Sa Ngiamsunthorn, P., ‘An abstract approach to domain perturbation for parabolic equations and parabolic variational inequalities’, Preprint, arXiv:1109.3257.Google Scholar
[12]Sa Ngiamsunthorn, P., ‘Invariant manifolds for parabolic equations under perturbation of the domain’, Preprint, arXiv:1109.3260.Google Scholar