When searching about PDE, I sometimes see the word "energy method". I want to know this method but there is no wikipedia page about it.
Is there a good web page or book about this topic?
2026-04-07 18:40:25.1775587225
What's energy method?
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Suppose we have a parabolic PDE. Basically we exploit the structure of the PDE to create an energy-like functional $E(t)$ that is non-increasing over time, giving an a-priori estimate for important quantities (like the $L^2$ norm) of the solution $u$ of our PDE. This can be used to prove uniqueness and other properties of $u$.
The first few pages of this lecture note has a nice example of the method. Most PDE textbooks also treat this subject quite well, e.g. Evans' Partial Differential Equations.