Cauchy problem of the Δ(k) operator related to the Diamond operator and the Laplace operator iterated k times

Given the Laplace operator Δ is defined by the Ultra-hyperbolic operator iterated k times k is defined by where p + q = n is the dimension of the Euclidean space ℝn. In this paper, we study Cauchy problem and fundamental solution of the Δ(k) operator by using Green's identity, In particular, Δ(...

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Main Author:	Bunpog,C.
Format:	Article
Published:	Eudoxus Press, LLC 2015
Subjects:	Computational Mathematics
Online Access:	http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=84885335136&origin=inward http://cmuir.cmu.ac.th/handle/6653943832/38706
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Institution:	Chiang Mai University

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spelling	th-cmuir.6653943832-387062015-06-16T07:54:00Z Cauchy problem of the Δ(k) operator related to the Diamond operator and the Laplace operator iterated k times Bunpog,C. Computational Mathematics Given the Laplace operator Δ is defined by the Ultra-hyperbolic operator iterated k times k is defined by where p + q = n is the dimension of the Euclidean space ℝn. In this paper, we study Cauchy problem and fundamental solution of the Δ(k) operator by using Green's identity, In particular, Δ(k) reduces to the Diamond operator if k = 1. Moreover, for q = 0 the ultra-hyperbolic operator 2 reduces to Δ, and Δ(k-1) reduces to the Laplace operator Δk iterated k times. © 2011 by Eudoxus Press,LLC All rights reserved. 2015-06-16T07:54:00Z 2015-06-16T07:54:00Z 2011-12-01 Article 15211398 2-s2.0-84885335136 http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=84885335136&origin=inward http://cmuir.cmu.ac.th/handle/6653943832/38706 Eudoxus Press, LLC
institution	Chiang Mai University
building	Chiang Mai University Library
country	Thailand
collection	CMU Intellectual Repository
topic	Computational Mathematics
spellingShingle	Computational Mathematics Bunpog,C. Cauchy problem of the Δ(k) operator related to the Diamond operator and the Laplace operator iterated k times
description	Given the Laplace operator Δ is defined by the Ultra-hyperbolic operator iterated k times k is defined by where p + q = n is the dimension of the Euclidean space ℝn. In this paper, we study Cauchy problem and fundamental solution of the Δ(k) operator by using Green's identity, In particular, Δ(k) reduces to the Diamond operator if k = 1. Moreover, for q = 0 the ultra-hyperbolic operator 2 reduces to Δ, and Δ(k-1) reduces to the Laplace operator Δk iterated k times. © 2011 by Eudoxus Press,LLC All rights reserved.
format	Article
author	Bunpog,C.
author_facet	Bunpog,C.
author_sort	Bunpog,C.
title	Cauchy problem of the Δ(k) operator related to the Diamond operator and the Laplace operator iterated k times
title_short	Cauchy problem of the Δ(k) operator related to the Diamond operator and the Laplace operator iterated k times
title_full	Cauchy problem of the Δ(k) operator related to the Diamond operator and the Laplace operator iterated k times
title_fullStr	Cauchy problem of the Δ(k) operator related to the Diamond operator and the Laplace operator iterated k times
title_full_unstemmed	Cauchy problem of the Δ(k) operator related to the Diamond operator and the Laplace operator iterated k times
title_sort	cauchy problem of the δ(k) operator related to the diamond operator and the laplace operator iterated k times
publisher	Eudoxus Press, LLC
publishDate	2015
url	http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=84885335136&origin=inward http://cmuir.cmu.ac.th/handle/6653943832/38706
_version_	1681421522178146304

Cauchy problem of the Δ(k) operator related to the Diamond operator and the Laplace operator iterated k times

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