Mass estimated in partial differential equation.

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What’s mass estimated in pde ?

The example we can integrate by mass estimated on space.

For $u_t(x, t)=u_{xx}(x, t)$ By maximum principle we have $u\le M$ aan nd $v\le N$.

So we can integrate $u_t$ on space say (0,1) for an easy choice.

That’s $\int^1_0u_t dx$ By mass estimated.

Some author say easy to see by mass estimated, that my question how use the mass estimated.