On the Operator ⨁Bk Related to Bessel Heat Equation
Author
Source
Mathematical Problems in Engineering
Issue
Vol. 2010, Issue 2010 (31 Dec. 2010), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2010-08-09
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
We study the equation (∂/∂t)u(x,t)=c2⊕Bku(x,t) with the initial condition u(x,0)=f(x) for x∈Rn+.
The operator ⊕Bk is the operator iterated k-times and is defined by ⊕Bk=((∑i=1pBxi)4-(∑j=p+1p+qBxi)4)k, where p+q=n is the dimension of the Rn+, Bxi=∂2/∂xi2+(2vi/xi)(∂/∂xi), 2vi=2αi+1, αi>-1/2, i=1,2,3,…,n, and k is a nonnegative integer, u(x,t) is an unknown function for (x,t)=(x1,x2,…,xn,t)∈Rn+×(0,∞), f(x) is a given generalized function, and c is a positive constant.
We obtain the solution of such equation, which is related to the spectrum and the kernel, which is so called Bessel heat kernel.
Moreover, such Bessel heat kernel has interesting properties and also related to the kernel of an extension of the heat equation.
American Psychological Association (APA)
Satsanit, Wanchak. 2010. On the Operator ⨁Bk Related to Bessel Heat Equation. Mathematical Problems in Engineering،Vol. 2010, no. 2010, pp.1-12.
https://search.emarefa.net/detail/BIM-476423
Modern Language Association (MLA)
Satsanit, Wanchak. On the Operator ⨁Bk Related to Bessel Heat Equation. Mathematical Problems in Engineering No. 2010 (2010), pp.1-12.
https://search.emarefa.net/detail/BIM-476423
American Medical Association (AMA)
Satsanit, Wanchak. On the Operator ⨁Bk Related to Bessel Heat Equation. Mathematical Problems in Engineering. 2010. Vol. 2010, no. 2010, pp.1-12.
https://search.emarefa.net/detail/BIM-476423
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-476423