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Can you give me an idea what is meant with dissipative partial differential equations?

I am no phycist (and do not know the difference between initial energy to final energy), but wikipedia told me that

A dissipative process is a process in which energy (internal, bulk flow kinetic, or system potential) is transformed from some initial form to some final form; the capacity of the final form to do mechanical work is less than that of the initial form. For example, heat transfer is dissipative because it is a transfer of internal energy from a hotter body to a colder one.

Now I wonder what a dissipative PDE means (mathematically).

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I think dissipative typically refers to a PDE with a highest spatial derivative of even number eg heat equation while dispersive refers to one with an odd derivative eg KdV see for example Whitams book

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    $\begingroup$ It is not as simple as looking at the spatial derivatives. The heat equation is dissipative (as you said), but the wave equation is not. The way the time derivatives enter the problem matters as well. $\endgroup$ – Ian Jul 21 '16 at 16:12

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