On Nonlinear Partial Differential Equations of Mixed Type

  In this talk we will discuss some recent developments in the study of nonlinear partial differential equations of mixed type, including the mixed parabolic-hyperbolic type and mixed elliptic-hyperbolic type. Examples include nonlinear degenerate diffusion-convection equations and transonic flow equations in fluid mechanics, as well as nonlinear equations of mixed type in a fluid mechanical formulation for isometric embedding problems in differential geometry. Further ideas, trends, and open problems in this direction will be also addressed.