Differential Operator Equations: A Method of Model Operators in the Theory of Boundary Value Problems

In this monograph, a wide range of problems of the theory of linear partial differential equations are considered from a unified point of view. The procedure of reducing a problem to a model differential operator equation of a special simple structure is studied. Classical and nonclassical equations and problems are compared. The spectral characteristics and properties of generalized solutions are considered for mixed-type and degenerating equations as well as for equations with discontinuous coefficients and equations containing a small parameter. Considerable attention is paid to the questions of the general theory of boundary problems. Necessary information is given from functional analysis and spectral theory of operators. For specialists in mathematical physics, functional analysis, and applied mathematics, as well as for senior students and postgraduates of relevant specialties.