Schauder bases and the decay rate of the heat equation View Full Text


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Article Info

DATE

2019-03-02

AUTHORS

José Bonet, Wolfgang Lusky, Jari Taskinen

ABSTRACT

We consider the classical Cauchy problem for the linear heat equation and integrable initial data in the Euclidean space RN. We show that given a weighted Lp-space Lwp(RN) with 1≤p<∞ and a fast-growing weight w, there are Schauder bases (en)n=1∞ in Lwp(RN) with the following property: given a positive integer m, there exists nm>0 such that, if the initial data f belong to the closed linear space of en with n≥nm, then the decay rate of the solution of the heat equation is at least t-m. Such a basis can be constructed as a perturbation of any given Schauder basis. The proof is based on a construction of a basis of Lwp(RN), which annihilates an infinite sequence of bounded functionals. More... »

PAGES

1-12

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URI

http://scigraph.springernature.com/pub.10.1007/s00028-019-00492-x

DOI

http://dx.doi.org/10.1007/s00028-019-00492-x

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https://app.dimensions.ai/details/publication/pub.1112505253


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