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Behaviour of the first eigenvalue of the p-Laplacian in a domain with a hole

100%

Sango M.

Colloquium Mathematicum

2001

tom 87

nr 1

103-111

We investigate the behaviour of a sequence $λ_{s}$, s = 1,2,..., of eigenvalues of the Dirichlet problem for the p-Laplacian in the domains $Ω_{s}$, s = 1,2,..., obtained by removing from a given domain Ω a set $E_{s}$ whose diameter vanishes when s → ∞. We estimate the deviation of $λ_{s}$ from the eigenvalue of the limit problem. For the derivation of our results we construct an appropriate asymptotic expansion for the sequence of solutions of the original eigenvalue problem.

Asymptotic analysis of the initial boundary value problem for the thermoelastic system in a perforated domain

100%

Sango M.

Colloquium Mathematicum

2003

tom 95

nr 1

91-115

We study the initial boundary value problem for the system of thermoelasticity in a sequence of perforated cylindrical domains $Q_{T}^{(s)}$, s = 1,2,... We prove that as s → ∞, the solution of the problem converges in appropriate topologies to the solution of a limit initial boundary value problem of the same type but containing some additional terms which are expressed in terms of quantities related to the geometry of $Q_{T}^{(s)}$. We give an explicit construction of that limit problem.

Ograniczanie wyników

2 Colloquium Mathematicum

2 Sango M.

1 2003

1 2001

Wyniki wyszukiwania

Behaviour of the first eigenvalue of the p-Laplacian in a domain with a hole

Asymptotic analysis of the initial boundary value problem for the thermoelastic system in a perforated domain