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The theory of complete generalized Jordan sets is employed to reduce the PDEwith the irreversible linear operator $B$ of finite index to the regularproblems. It is demonstrated how the question of the choice of boundaryconditions is connected with the $B$-Jordan structure of coefficients of PDE.The various approaches shows the combination alternative Lyapunov method,Jordan structure coefficients and skeleton decomposition of irreversible linearoperator from the main part equation are among the most powerfull methods toattack such challenging problem. On this base the complex problem of the {\itcorrect choice of boundary conditions} for the wide class of the singular PDEcan be solved. Aggregated existence and uniqueness theorems can be proved,solution may continuously depend on the function determied from theexperiments. Such theory can be applied to the integral--differential equationswith partial derivatives.

Irregular linear systems of PDEs with the conditions on solutions' projections