IJPAM: Volume 93, No. 1 (2014)

ON THE GENERALIZED NONLINEAR
DIAMOND HEAT KERNEL

Wanchak Satsanit
Department of Mathematics
Faculty of Science, Maejo University
Chiangmai, 50290, THAILAND


Abstract. In this paper, we study the nonlinear heat equation

\begin{displaymath}\notag\
\frac{\partial}{\partial t}\,\triangle^{k} u(x,t)-c^2\diamondsuit^{k}u(x,t)=f(x,t,u(x,t)),
\end{displaymath}  

where $\triangle^{k}$ is the Laplacian operator iterated $k-$ times and is defined by (1.4)and $\diamondsuit^{k}$ is the Diamond operator iterated $k-$ times and is defined by (1.2). We obtain an interesting kernel related to the nonlinear heat equation.

Received: September 15, 2013

AMS Subject Classification:

Key Words and Phrases: Fourier transform, spectrum, diamond operator

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DOI: 10.12732/ijpam.v93i1.4 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 93
Issue: 1
Pages: 31 - 43

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).