# Almost conserved

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An **almost conserved** quantity is one whose derivative in time is not exactly zero, but is somehow ``small* or ``low-order* enough that the growth of the quantity can be controlled in time (perhaps by some variant of Gronwall's inequality).

A common way to create an almost conserved quantity is to start with a conservation law and insert a spatial or frequency weight.

The I-method relies heavily on the construction of an almost conserved quantity.

An important variant of an almost conserved quantity is a monotone quantity.