ИСТИНА

We consider mixed type second order linear PDEs on the plane and analyze invariants of their main symbols up to smooth or sufficiently smooth changes of coordinates and multiplication nonvanishing functions. Such invariants have both local and nonlocal nature. The local ones were described in the end of last century for a generic cases. The complete description of smooth nonlocal invariants is open problem even for simplest configurations of characteristic net, while for such configurations topologically there are no invariants of characteristic net at all. The talk is devoted to these results and recent achievements in this area.