What does 'dissipative PDE' means? 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).

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 
