On the diamond operator related to the wave equation
In this paper, we study the solution of the equation ◇ku(x) = f (x) where ◇k is the Diamond operator iterated k times and is defined by ◇k ((∑i=1p ∂2/∂xi2)2 -(∑j=p+1p+q ∂2/∂xj2)2)k where p+q = n is the dimension of the n-dimensional Euclidean space Rn, x = (x1, x2, ..., xn) ∈ Rn, k is a nonnegative...
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th-cmuir.6653943832-47922014-08-30T02:55:46Z On the diamond operator related to the wave equation Kananthai A. In this paper, we study the solution of the equation ◇ku(x) = f (x) where ◇k is the Diamond operator iterated k times and is defined by ◇k ((∑i=1p ∂2/∂xi2)2 -(∑j=p+1p+q ∂2/∂xj2)2)k where p+q = n is the dimension of the n-dimensional Euclidean space Rn, x = (x1, x2, ..., xn) ∈ Rn, k is a nonnegative integer, u(x) is an unknown and f is a generalized function. It is found that the solution u(x) depends on the conditions of p and q and moreover such a solution is related to the solution of the Laplace equation and the wave equation. 2014-08-30T02:55:46Z 2014-08-30T02:55:46Z 2001 Article 0362546X 10.1016/S0362-546X(01)00272-3 58358 NOAND http://www.scopus.com/inward/record.url?eid=2-s2.0-0035425986&partnerID=40&md5=1e02c1a1882767e2eb169871cbb334f2 http://cmuir.cmu.ac.th/handle/6653943832/4792 English |
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In this paper, we study the solution of the equation ◇ku(x) = f (x) where ◇k is the Diamond operator iterated k times and is defined by ◇k ((∑i=1p ∂2/∂xi2)2 -(∑j=p+1p+q ∂2/∂xj2)2)k where p+q = n is the dimension of the n-dimensional Euclidean space Rn, x = (x1, x2, ..., xn) ∈ Rn, k is a nonnegative integer, u(x) is an unknown and f is a generalized function. It is found that the solution u(x) depends on the conditions of p and q and moreover such a solution is related to the solution of the Laplace equation and the wave equation. |
| format |
Article |
| author |
Kananthai A. |
| spellingShingle |
Kananthai A. On the diamond operator related to the wave equation |
| author_facet |
Kananthai A. |
| author_sort |
Kananthai A. |
| title |
On the diamond operator related to the wave equation |
| title_short |
On the diamond operator related to the wave equation |
| title_full |
On the diamond operator related to the wave equation |
| title_fullStr |
On the diamond operator related to the wave equation |
| title_full_unstemmed |
On the diamond operator related to the wave equation |
| title_sort |
on the diamond operator related to the wave equation |
| publishDate |
2014 |
| url |
http://www.scopus.com/inward/record.url?eid=2-s2.0-0035425986&partnerID=40&md5=1e02c1a1882767e2eb169871cbb334f2 http://cmuir.cmu.ac.th/handle/6653943832/4792 |
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