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- W1961508306 abstract "Let u(x,t)be the temperature at position x in R 3 and at time t≥0. For N=1,2,3,... let w 1 N ,w 2 N ,...,w N N , be a sequence of points in R 3 and let D N be the domain in R 3 defined by $${D^N} = bigcaplimits_{j = 1}^N {left( {xleft| {left| {x - w_j^N} right|} right. > frac{alpha }{N}} right)} $$(1)where α is a fixed positive constant. The temperature u satisfies the initial-boundary value problem $$frac{{partial u}}{{partial t}} = Delta uin{D^N},t > 0$$(2)$$u(x,0) = f(x)forxin{D^N}andu(x,t) = 0;on;B_j^Nfort > 0,j = 1,2,3,...,N$$(3)Here f (x) is a smooth, positive function of compact support representing the initial temperature distribution and B j N is the sphere centered at w j N with radius α/N." @default.
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- W1961508306 date "1987-01-01" @default.
- W1961508306 modified "2023-09-22" @default.
- W1961508306 title "The point interaction approximation for diffusion in regions with many small holes" @default.
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- W1961508306 doi "https://doi.org/10.1007/978-3-642-46599-4_16" @default.
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