Darbu - gurs - bodo problem analog in classes of generalized fuctions for systems of differential partial equations with constant coefficients

Partial differential equations with constant coefficients are considered in the paper aiming at the proof of the Malgrangian's second theorem analog. The proof of the theorem about the boundary-value problem analog solvability in classes of generalized functions of finite order is also the aim of the paper as well as the proof of theorems about the solution existence and uniqueness of a boundary-value problem in a special space of generalized functions of finite order. As a result problems and formulations of the correct solvability of Darbu-Gurs-Bodo problem analogs in classes of generalized functions of finite and infinite orders have been investigated. The Malgrangian's second theorem analog for special classes of generalized functions of many variables has been proved. Conditions on a characteristic set on a non-characteristic part of a characteristic set for a system of partial equations with constant coefficients, ensuring the continuation of generalized solutions in a class of generalized functions of finite and infinite orders have been obtained as well as conditions for the uniqueness of the Darbu-Gurs-Bodo problem solution in classes of generalized functionsAvailable from VNTIC / VNTIC - Scientific & Technical Information Centre of RussiaSIGLERURussian Federatio