On the operator ⊗<inf>B</inf><sup>k</sup>Related 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.6653943832-492272018-08-16T02:12:48Z On the operator ⊗<inf>B</inf><sup>k</sup>Related to the Bessel heat equation Eakachai Suntonsinsoungvon Amnuay Kananthai Mathematics 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. 2018-08-16T02:12:48Z 2018-08-16T02:12:48Z 2009-12-01 Journal 13118080 2-s2.0-78649783617 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=78649783617&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/49227 |
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Mathematics Eakachai Suntonsinsoungvon Amnuay Kananthai On the operator ⊗<inf>B</inf><sup>k</sup>Related to the Bessel heat equation |
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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. |
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Eakachai Suntonsinsoungvon Amnuay Kananthai |
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Eakachai Suntonsinsoungvon Amnuay Kananthai |
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Eakachai Suntonsinsoungvon |
title |
On the operator ⊗<inf>B</inf><sup>k</sup>Related to the Bessel heat equation |
title_short |
On the operator ⊗<inf>B</inf><sup>k</sup>Related to the Bessel heat equation |
title_full |
On the operator ⊗<inf>B</inf><sup>k</sup>Related to the Bessel heat equation |
title_fullStr |
On the operator ⊗<inf>B</inf><sup>k</sup>Related to the Bessel heat equation |
title_full_unstemmed |
On the operator ⊗<inf>B</inf><sup>k</sup>Related to the Bessel heat equation |
title_sort |
on the operator ⊗<inf>b</inf><sup>k</sup>related to the bessel heat equation |
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2018 |
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https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=78649783617&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/49227 |
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