Well-posedness of a boundary value problem for a class of third-order operator-differential equations
1 Baku State University, 23 Z. Khalilov St., Baku, 1148, Azerbaijan
2 Institute of Mathematics and Mechanics of NAS of Azerbaijan, 9 B. Vahabzadeh St., Baku, 1141, Azerbaijan
3 Helwan University, Ain Helwan, Cairo, 11795, Egypt
Boundary Value Problems 2013, 2013:140 doi:10.1186/1687-2770-2013-140Published: 30 May 2013
This paper investigates the well-posedness of a boundary value problem on the semiaxis for a class of third-order operator-differential equations whose principal part has multiple real characteristics. We obtain sufficient conditions for the existence and uniqueness of the solution of a boundary value problem in the Sobolev-type space . These conditions are expressed in terms of the operator coefficients of the investigated equation. We find relations between the estimates of the norms of intermediate derivatives operators in the subspace and the solvability conditions. Furthermore, we calculate the exact values of these norms. The results are illustrated with an example of the initial-boundary value problems for partial differential equations.
MSC: 34G10, 47A50, 47D03, 47N20.