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?

  • 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

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.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.