On the operator bk related to the bessel heat equation
In this paper, we study the equation ∂/∂t u(x, t) = c2Bk u(x, t) with the initial condition u(x, 0) = f(x) for x ∈ ℝn+, where the operator Bk is defined by Bk = [(Bx1 + ⋯ B xp)3 + (Bxp+1 + ⋯ + B xp-q)3]k, p+q = n is the dimension of the space ℝ2+ = {x = (x1, x2,. . . xn) : x1 > 0, x2 > 0, . ....
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th-cmuir.6653943832-509712018-09-04T04:49:08Z On the operator bk related to the bessel heat equation Somboon Niyom Amnuay Kananthai Mathematics In this paper, we study the equation ∂/∂t u(x, t) = c2Bk u(x, t) with the initial condition u(x, 0) = f(x) for x ∈ ℝn+, where the operator Bk is defined by Bk = [(Bx1 + ⋯ B xp)3 + (Bxp+1 + ⋯ + B xp-q)3]k, p+q = n is the dimension of the space ℝ2+ = {x = (x1, x2,. . . xn) : x1 > 0, x2 > 0, . . . ,xn > 0}, Bx1 = ∂2/∂xi2 + 2v i/xi ∂/∂xi, 2vi = 2αi + 1, αi > -1/2, i = 1, 2,..., n, u(x, t) is an unknown function for (x, t) = [x1, x2,...,x n, t) ∈ ℝn+×(0, ∞), f(x) is a 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 heat kernel. Moreover, such Bessel heat kernel has interesting properties and also related to the kernel of an extension of the heat equation. © 2010 Academic Publications. 2018-09-04T04:49:08Z 2018-09-04T04:49:08Z 2010-12-13 Journal 13118080 2-s2.0-78649863296 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=78649863296&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/50971 |
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Mathematics Somboon Niyom Amnuay Kananthai On the operator bk related to the bessel heat equation |
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In this paper, we study the equation ∂/∂t u(x, t) = c2Bk u(x, t) with the initial condition u(x, 0) = f(x) for x ∈ ℝn+, where the operator Bk is defined by Bk = [(Bx1 + ⋯ B xp)3 + (Bxp+1 + ⋯ + B xp-q)3]k, p+q = n is the dimension of the space ℝ2+ = {x = (x1, x2,. . . xn) : x1 > 0, x2 > 0, . . . ,xn > 0}, Bx1 = ∂2/∂xi2 + 2v i/xi ∂/∂xi, 2vi = 2αi + 1, αi > -1/2, i = 1, 2,..., n, u(x, t) is an unknown function for (x, t) = [x1, x2,...,x n, t) ∈ ℝn+×(0, ∞), f(x) is a 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 heat kernel. Moreover, such Bessel heat kernel has interesting properties and also related to the kernel of an extension of the heat equation. © 2010 Academic Publications. |
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Somboon Niyom Amnuay Kananthai |
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Somboon Niyom Amnuay Kananthai |
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Somboon Niyom |
title |
On the operator bk related to the bessel heat equation |
title_short |
On the operator bk related to the bessel heat equation |
title_full |
On the operator bk related to the bessel heat equation |
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On the operator bk related to the bessel heat equation |
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On the operator bk related to the bessel heat equation |
title_sort |
on the operator bk 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=78649863296&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/50971 |
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