Talk:Weak solution

Excellent Format

I just wanted to say that the format for this article, that is to give a simple example before the general formulation, is great. It allows for a continuous reading from top to bottom (as short as the article may be) without having to browse around putting bits and pieces together. Hamsterlopithecus (talk) 20:36, 13 May 2009 (UTC)

Mild solution

Is a mild solution the same as a weak solution? Are these terms synonymic, or they are not?--Бертран (talk) 20:52, 18 March 2011 (UTC)

Distributions

In mathematics, a weak solution (also called a generalized solution) [..] is a function [..]. There are many different definitions of weak solution [and] one of the most important is based on the notion of distributions.

The lead seems unclear: is a weak solution necessarily a function, or can it be any distribution? Cesiumfrog (talk) 08:30, 3 January 2016 (UTC)

More examples

I think a few examples besides the one given would be much more useful to understand what was presented in the general case. A number of simple examples showing P(x, D)u(x), a_alpha1... and D^alpha1... for simple partial differential equations such as the Helmholtz Equation or Elasticity Equation. Most of us are not mathematicians and instead of trying to become one rely on others to bring their knowledge to those less skilled in the art, like me.

Thanks Pete1314 (talk) 02:30, 31 March 2016 (UTC)

I agree – in particular I think an example of an ordinary differential equation would be nice, to complement the current example of a partial differential equation. Joel Brennan (talk) 09:14, 22 July 2021 (UTC)

Hmm Also the SDE examples I think are not relevant actually, I think we should delete them? a weak solution for an SDE is quite a different concept that doesnt involve test functions or integration by parts, its more about a solution in a different measure space / initial condition https://stevensoojin.kim/blog/weak-solutions/ Vargfran (talk) 23:43, 11 June 2026 (UTC)