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I am searching for a reference where weak formulation accure algebraicly, I found in Wikipedia a genral concept for weak formulation which goes from duality, you can see it(here) .

But I want another reference in literature , all what I get is about PDE weak formulation using integrals. Can someone help? I want a reference to this genral concept.

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  • $\begingroup$ Maybe you do not want weak solution, but distributional solutions? There, the dual products are mainly used (instead of integrals, since solutions are not regular enough). $\endgroup$
    – Cahn
    Commented Nov 14, 2020 at 23:46

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