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The Analysis of the Two-dimensional Diffusion Equation With a Source

Author(s): Victor Onomza WAZIRI | Sunday Augustus REJU

Journal: Leonardo Electronic Journal of Practices and Technologies
ISSN 1583-1078

Volume: 5;
Issue: 9;
Start page: 43;
Date: 2006;
Original page

Keywords: Maximum principle | Hamiltonian function | Fourier series | energized wave equation and Simulates

This study presents a new variant analysis and simulations of the two-dimensional energized wave equation remarkably different from the diffusion equations studied earlier studied. The objective functional and the dynamical energized wave are penalized to form a function called the Hamiltonian function. From this function, we obtained the necessary conditions for the optimal solutions using the maximum principle. By applying the Fourier solution to the first order differential equation, the analytical solutions for the state and control are obtained. The solutions are simulated to give visual physical interpretation of the waves and the numerical values.
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