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Article information
2004 , Volume 9, ¹ 1, p.3-10
Nonlaopon K., Kananthai A.
On the generalized heat kernel
We study the equation
with the initial condition
for - n -dimensional Euclidean space. The operator denotes the Laplace operator iterated k-times and defined by
where n - is the dimension of the Euclidean space ; , u(x,t) is an unknown function, (x, t) = ; f(x) - is the given generalized function, k is a nonnegative integer and c is a positive constant. We obtain the solution of such equation which is so called the generalized heat kernel if t is a time and x is a position. Moreover, such the generalized heat kernel has interesting properties and also related to the solution of heat equation.
[full text] Classificator Msc2000:- *35K30 Initial value problems for higher-order, parabolic equations
- 35M20 PDE of composite type
Keywords: Fourier transform, convolution
Author(s):
Nonlaopon K
Office: Chiangmai University, Department of Mathematics, Thailand
Address: Thailand, Chiangmai
E-mail: Kamsingn@yahoo.com
Kananthai A
Office: Chiangmai University
Address: Thailand, Chiangmai
E-mail: malamnka@science.cmu.ac.th
Bibliography link:
Nonlaopon K., Kananthai A. On the generalized heat kernel // Computational technologies. 2004. V. 9. ¹ 1. P. 3-10
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