Asymptotic Behaviour of the Fundamental Solution to ∂u/∂t = — ( — ∆) m u

X LI; R WONG

doi:10.1098/rspa.1993.0071

Asymptotic Behaviour of the Fundamental Solution to ∂u/∂t = — ( — ∆) ^m u

X LI
, R WONG

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

Abstract

An asymptotic expansion is derived for the Fourier integral

f^{^}(x)= ¹⁄_(2π)n/2∫_Rnexp(−|q|^2m+ix⋅q)dq, xεℝⁿ

as |x| →∞, where m is a positive integer. From this, it is deduced that the fundamental solution to the ‘heat’ equation

∂u/∂t=−(−Δ)mu

has an infinite number of zeros tending to infinity.

Original language	English
Pages (from-to)	423-432
Journal	Royal Society of London. Proceedings A. Mathematical, Physical and Engineering Sciences
Volume	441
Issue number	1912
DOIs	https://doi.org/10.1098/rspa.1993.0071
Publication status	Published - 8 May 1993
Externally published	Yes

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@article{37621acd410f4e479655fac4b9f9f2ce,

title = "Asymptotic Behaviour of the Fundamental Solution to ∂u/∂t = — ( — ∆) m u",

abstract = "An asymptotic expansion is derived for the Fourier integral f\textasciicircum{}(x)= 1⁄(2π)n/2 ∫Rn exp(−|q|2m+ix⋅q)dq, xεℝn as |x| →∞, where m is a positive integer. From this, it is deduced that the fundamental solution to the {\textquoteleft}heat{\textquoteright} equation ∂u/∂t=−(−Δ)mu has an infinite number of zeros tending to infinity.",

author = "X LI and R WONG",

year = "1993",

month = may,

day = "8",

doi = "10.1098/rspa.1993.0071",

language = "English",

volume = "441",

pages = "423--432",

journal = "Royal Society of London. Proceedings A. Mathematical, Physical and Engineering Sciences",

issn = "1364-5021",

publisher = "The Royal Society Publishing",

number = "1912",

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TY - JOUR

T1 - Asymptotic Behaviour of the Fundamental Solution to ∂u/∂t = — ( — ∆) m u

AU - LI, X

AU - WONG, R

PY - 1993/5/8

Y1 - 1993/5/8

N2 - An asymptotic expansion is derived for the Fourier integral f^(x)= 1⁄(2π)n/2 ∫Rn exp(−|q|2m+ix⋅q)dq, xεℝn as |x| →∞, where m is a positive integer. From this, it is deduced that the fundamental solution to the ‘heat’ equation ∂u/∂t=−(−Δ)mu has an infinite number of zeros tending to infinity.

AB - An asymptotic expansion is derived for the Fourier integral f^(x)= 1⁄(2π)n/2 ∫Rn exp(−|q|2m+ix⋅q)dq, xεℝn as |x| →∞, where m is a positive integer. From this, it is deduced that the fundamental solution to the ‘heat’ equation ∂u/∂t=−(−Δ)mu has an infinite number of zeros tending to infinity.

U2 - 10.1098/rspa.1993.0071

DO - 10.1098/rspa.1993.0071

M3 - RGC 21 - Publication in refereed journal

SN - 1364-5021

VL - 441

SP - 423

EP - 432

JO - Royal Society of London. Proceedings A. Mathematical, Physical and Engineering Sciences

JF - Royal Society of London. Proceedings A. Mathematical, Physical and Engineering Sciences

IS - 1912

ER -