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- Title
Boundary value problem for a third-order equation of mixed type in a rectangular domain.
- Authors
Sabitov, K.
- Abstract
For a third-order equation of the parabolic-hyperbolic type, we suggest a method for studying a boundary value problem by solving the inverse problem for a second-order equation of the mixed parabolic-hyperbolic type with unknown right-hand side depending implicitly on time. We prove a criterion for the uniqueness of the solution of the boundary value problem constructed in the form of the sum of a series in the eigenfunctions of the corresponding one-dimensional Sturm-Liouville problem. We prove the stability of the solution with respect to the boundary data in the norms of the spaces W [0, 1] and $$C\left( {\bar D} \right)$$.
- Subjects
BOUNDARY value problems; EIGENFUNCTIONS; NUMERICAL solutions to Sturm-Liouville equations; INVERSE problems; NUMERICAL solutions to differential equations
- Publication
Differential Equations, 2013, Vol 49, Issue 2, p187
- ISSN
0012-2661
- Publication type
Article
- DOI
10.1134/S0012266113020055