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Far East Journal of Applied Mathematics

where is the Diamond operator iterated k-times, defined by

is the dimension of the Euclidean space is an unknown for k is a positive integer and c is a positive constant.

On the suitable conditions for f, u and for the spectrum of the Diamond heat kernel, we can find the unique solution in the compact subset of

Moreover, if we put

and

then we obtain the solution of nonlinear equation related to the heat equation.

Far East Journal of Applied Mathematics
Volume 24, Issue 2, Pages 149 - 161 (August 2006)

ON THE GENERALIZED NONLINEAR DIAMOND HEAT EQUATION RELATED TO THE SPECTRUM
G. Sritanratana (Thailand) and A. Kananthai (Thailand)

Abstract:
In this paper, we study the nonlinear equation of the form

where is the Diamond operator iterated k-times, defined by

is the dimension of the Euclidean space is an unknown for k is a positive integer and c is a positive constant.

On the suitable conditions for f, u and for the spectrum of the Diamond heat kernel, we can find the unique solution in the compact subset of

Moreover, if we put

and

then we obtain the solution of nonlinear equation related to the heat equation.

Keywords and phrases: the nonlinear equation, the spectrum, the diamond heat kernel.

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