On the operator ⊗BkRelated to the Bessel heat equation
In this article, we study the equation ∂/∂t u(x, t) = c 2⊗Bk u(x, t) with the initial condition u(x, 0) = f(x) for x ∈ ℝn+, where the operator ⊗Bk is deflned by ⊗Bk = [(Bx1 +⋯+ Bxp)3 - (BXp+1 +⋯+ BXp+q)3]k, p + q = n is the dimension of the space ℝn+, Bxi = ∂2/∂xi2 + 2vi/x i ∂/ ∂xi, 2vi = 2αi + 1, α...
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th-cmuir.6653943832-57352014-08-30T03:23:24Z On the operator ⊗BkRelated to the Bessel heat equation Suntonsinsoungvon E. Kananthai A. In this article, we study the equation ∂/∂t u(x, t) = c 2⊗Bk u(x, t) with the initial condition u(x, 0) = f(x) for x ∈ ℝn+, where the operator ⊗Bk is deflned by ⊗Bk = [(Bx1 +⋯+ Bxp)3 - (BXp+1 +⋯+ BXp+q)3]k, p + q = n is the dimension of the space ℝn+, Bxi = ∂2/∂xi2 + 2vi/x i ∂/ ∂xi, 2vi = 2αi + 1, αi > -1/2, xi > 0, i = 1, 2,... ,n, u(x,t) is an unknown function for (x,t) = (x1, x2,..., xn,t) ∈ ℝn+ × (0, ∞), f(x) is a given generalized function, k is a positive integer and c is a positive constant. We obtain the solution of such equation which is related to the spectrum and the kernel. Moreover, such Bessel heat kernel has interesting properties and also related to the kernel of an extension of the heat equation. © 2009 Academic Publications. 2014-08-30T03:23:24Z 2014-08-30T03:23:24Z 2009 Article 13118080 http://www.scopus.com/inward/record.url?eid=2-s2.0-78649783617&partnerID=40&md5=857a0effb6e482c820fc98def6bf580a http://cmuir.cmu.ac.th/handle/6653943832/5735 English |
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In this article, we study the equation ∂/∂t u(x, t) = c 2⊗Bk u(x, t) with the initial condition u(x, 0) = f(x) for x ∈ ℝn+, where the operator ⊗Bk is deflned by ⊗Bk = [(Bx1 +⋯+ Bxp)3 - (BXp+1 +⋯+ BXp+q)3]k, p + q = n is the dimension of the space ℝn+, Bxi = ∂2/∂xi2 + 2vi/x i ∂/ ∂xi, 2vi = 2αi + 1, αi > -1/2, xi > 0, i = 1, 2,... ,n, u(x,t) is an unknown function for (x,t) = (x1, x2,..., xn,t) ∈ ℝn+ × (0, ∞), f(x) is a given generalized function, k is a positive integer and c is a positive constant. We obtain the solution of such equation which is related to the spectrum and the kernel. Moreover, such Bessel heat kernel has interesting properties and also related to the kernel of an extension of the heat equation. © 2009 Academic Publications. |
| format |
Article |
| author |
Suntonsinsoungvon E. Kananthai A. |
| spellingShingle |
Suntonsinsoungvon E. Kananthai A. On the operator ⊗BkRelated to the Bessel heat equation |
| author_facet |
Suntonsinsoungvon E. Kananthai A. |
| author_sort |
Suntonsinsoungvon E. |
| title |
On the operator ⊗BkRelated to the Bessel heat equation |
| title_short |
On the operator ⊗BkRelated to the Bessel heat equation |
| title_full |
On the operator ⊗BkRelated to the Bessel heat equation |
| title_fullStr |
On the operator ⊗BkRelated to the Bessel heat equation |
| title_full_unstemmed |
On the operator ⊗BkRelated to the Bessel heat equation |
| title_sort |
on the operator ⊗bkrelated to the bessel heat equation |
| publishDate |
2014 |
| url |
http://www.scopus.com/inward/record.url?eid=2-s2.0-78649783617&partnerID=40&md5=857a0effb6e482c820fc98def6bf580a http://cmuir.cmu.ac.th/handle/6653943832/5735 |
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1681420481642627072 |