= Control theory
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This basically adds one more ingredient to <partial differential equations>: a <function> that we can select.
And then the question becomes: if this function has such and such limitation, can we make the solution of the <differential equation> have such and such property?
It's quite fun from a mathematics point of view!
Control theory also takes into consideration possible <discretization> of the domain, which allows using <numerical methods to solve partial differential equations>, as well as digital, rather than analogue control methods.