Group analysis of the heat-conduction equation in displacements of isothermal surfaces. 2. Obtaining invariant solutions of boundary-value problems

1988 ◽  
Vol 54 (1) ◽  
pp. 100-103
Author(s):  
N. M. Tsirel'man
Keyword(s):  
Heat Conduction ◽  
Boundary Value Problems ◽  
Heat Conduction Equation ◽  
Boundary Value ◽  
Group Analysis ◽  
Conduction Equation ◽  
Invariant Solutions

scholarly journals A Class of Integral Transforms

1964 ◽  
Vol 14 (1) ◽  
pp. 33-40 ◽  
Author(s):  
Jet Wimp
Keyword(s):  
Heat Conduction ◽  
Boundary Value Problems ◽  
Inversion Formula ◽  
Heat Conduction Equation ◽  
Boundary Value ◽  
Integral Transforms ◽  
Conduction Equation ◽  
New Class ◽  
Special Cases ◽  
Image Position

In this paper we discuss a new class of integral transforms and their inversion formula. The kernel in the transform is a G-function (for a treatment of this function, see ((1), 5.3) and integration is performed with respect to the argument of that function. In the inversion formula, the kernel is likewise a G-function, but there integration is performed with respect to a parameter. Known special cases of our results are the Kontorovitch-Lebedev transform pair ((2), v. 2; (3))and the generalised Mehler transform pair (7)These transforms are used in solving certain boundary value problems of the wave or heat conduction equation involving wedge or conically-shaped boundaries, and are extensively tabulated in (6).

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