Evolution Inclusions and Variation Inequalities for Earth Data Processing I : Operator Inclusions and Variation Inequalities for Earth Data Processing Here the authors present modern mathematical methods to solve problems of differential operator inclusions and evolution variation inequalities which may occur in fields such as geophysics aerohydrodynamics or fluid dynamics. For the first time they describe the detailed generalization of various approaches to the analysis of fundamentally nonlinear models and provide a toolbox of mathematical equations. These new mathematical methods can be applied to a broad spectrum of problems. Examples of these are phase changes diffusion of electromagnetic acoustic vibro hydro and seismoacoustic waves or quantum mechanical effects. This is the first of two volumes dealing with the subject.