Math Seminar "Mathematical Models and Integration Methods"

Annotation We propose a regular method for generating consistent systems of partial differential equations (PDEs) that describe  a wide class of models in natural sciences. Such systems appear within typical constructions of the Homological  Algebra as complexes of differential operators describing compatibility conditions for overdetermined PDEs.  Additional assumptions on the ellipticity/parameter-dependent ellipticity of the  differential complexes provide a  wide range of elliptic, parabolic and hyperbolic operators. In particular, most equations related to modern  Mathematical Physics are generated by the de Rham complex of differentials on exterior differential forms.  These includes the equations based on elliptic Laplace and Lam\'e type operators; the parabolic heat and mass  transfer equations; the Euler type and Navier-Stokes type equations in Hydrodynamics; the hyperbolic wave equation  and the Maxwell equations in Electrodynamics; the Klein-Gordon equation