Composite Type Equations and Inverse Problems

Part 1 Composite type equations as the original mathematical object: equations of the composite type in mathematics and mathematical simulation; canonical types of third order; boundary-value problems for third order equations of composite type; hyperbolic boundary-value problem uniqueness of regular solutions; existence of the regularized solutions of the hyperbolic boundary-value problem; the elliptic boundary-value problem; uniqueness of regular solutions; existence of generalized solutions of the elliptic boundary-value problem; existence of regular solutions of the elliptic boundary-value problem; correlation of the hyperbolic and elliptic boundary-value problems; remark on the third order equations of the variable direction; nonlocal problems for equations of composite type. Part 2 Solvability of inverse problems and other applications: inverse problems for equations with partial derivatives; linear inverse problems for elliptic and parabolic equations; on solvability of nonlinear inverse problems; solvability of nonclassical boundary-value problems for equations of second order and third order; the mixed problem for second order equations not solved for the time derivative; boundary-value problems for the second order equations of the mixed type; the problem with oblique derivative for equations of second and third orders; a problem of viscous elasticity and the third order equation in noncylindrical domains connected with this problem.