Composite Type Equations and Inverse Problems

Abstract

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.