Is Sami Groupes Theory the Best Method for Solving Parabolic Problems?

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What are some methods of solving parabolic PDEs apart from separation of variables and numerical methods?
 
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Fourier and Laplace transforms, self-similiar variables, symmetries, energy methods, etc...

There are plenty of techniques, so I ask you: in what level of skill are we talking about?
 
sami groupes theory, it is the best method for solving parabolic problem
 

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