Multi-Weighted Parabolic Equations and Systems

We introduce multi-weighted parabolic operators and show that the class of such operators is closed under compositions. We prove the solvability of initial-value problems for multi-weighted parabolic equations in anisotropic Sobolev-Slobodetsky spaces and also for multi-weighted parabolic systems that are simultaneously multi-order systems relative to the spatial variables. Bibliography: 15 titles.