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Home  >  Volume 40

Scaling Invariant Transformation on Optimal Control Problem by Odio A.O.(pages 1-4)
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Analytical solution by scale invariant approach to non-linear diffusion as a control problem is carefully studied. Non-linear diffusion is characterized by the partial differential equation. 

Where D(u) is the diffusion coefficient and when D(u) = un, this equation is known as the porous medium equation. Scaling grouping are introduced to reduce the original equations to ordinary differential equation. Self-similar solutions can be found for all n>0 in the case of the porous medium equation. 

As an illustration for the porous medium equation for n=5, numerical values are obtained for some parameters by the sealing invariant method. 

Key Words: Optimal control problem, non-linear diffusion, scaling grouping, porous medium equation, self-similar solution, diffusion coefficient.