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?
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1$\begingroup$ You can check The Energy Method, Stability, and Nonlinear Convection (Applied Mathematical Sciences) 2nd Edition for a comprehensive introduction. $\endgroup$ – Artem Dec 21 '18 at 22:34
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Suppose we have a parabolic PDE, says. Basically we exploit the structure of the PDE to create an energy-like functional $E(t)$ that is non-increasing over time, giving a priori estimate for important quantities (like $L^2$ 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.
