HIGHER ORDER APPROXIMATIONS IN THE HEAT EQUATION AND THE TRUNCATED MOMENT PROBLEM

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In this paper, we employ linear combinations of n heat kernels to approximate solutions to the heat equation. We show that such approximations are of order O(t(1/2p - 2n+1/2)) in L(p)-norm, 1 <= p <= infinity, as t -> infinity. For positive solutions of the heat equation such approximations are achieved using the theory of truncated moment problems. For general sign-changing solutions these type of approximations are obtained by simply adding an auxiliary heat kernel. Furthermore, inspired by numerical computations, we conjecture that such approximations converge geometrically as n -> infinity for any fixed t > 0.
Publisher
SIAM PUBLICATIONS
Issue Date
2009-02
Language
English
Article Type
Article
Keywords

SCALAR CONSERVATION-LAWS; LARGE TIME BEHAVIOR; ASYMPTOTIC-BEHAVIOR; DIFFUSION-EQUATIONS; N-WAVES; BURGERS-EQUATION; CONVERGENCE

Citation

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, v.40, no.6, pp.2241 - 2261

ISSN
0036-1410
DOI
10.1137/08071778X
URI
http://hdl.handle.net/10203/98405
Appears in Collection
MA-Journal Papers(저널논문)
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