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
 
Thread 'Direction Fields and Isoclines'

Thread 'Direction Fields and Isoclines'

I sketched the isoclines for $$ m=-1,0,1,2 $$. Since both $$ \frac{dy}{dx} $$ and $$ D_{y} \frac{dy}{dx} $$ are continuous on the square region R defined by $$ -4\leq x \leq 4, -4 \leq y \leq 4 $$ the existence and uniqueness theorem guarantees that if we pick a point in the interior that lies on an isocline there will be a unique differentiable function (solution) passing through that point. I understand that a solution exists but I unsure how to actually sketch it. For example, consider a...
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