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Title: Singular limit in a parabolic equation
Authors: Dłotko, Tomasz
Keywords: parabolic equation; boundary conditions
Issue Date: 1993
Citation: Demonstratio Mathematica, Vol. 26, nr 2 (1993) s. 473-481
Abstract: Our aim here is to study the singular limit, when e —• 0, in a parabolic problem ' ut = s2Au +f(t,u), x € Í2 C Rn, f > 0, (1) u(0,x) = t¿o(a;) for x £ Í2, Bu = 0 for x e dQ, with a bounded smooth domain Q, £ > 0 and the boundary operator B of either the Dirichlet type (B = Id) or the Neumann type (B = n is the normal vector to dQ). We want to estimate the difference between u and the solution y — y(t,x) of the limit problem (2) ÍVt = f(t,y), t> 0, \»(0,a:) = «o(a), x £ Í2, the central interest being estimates on bounded time interval [0,T]. The problem of long time behaviour (when t —> oo) of a pair u, y has been considered previously, e.g. in [4, 7] (Fragment tekstu).
DOI: 10.1515/dema-1993-0218
ISSN: 2391-4661
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