Affiliation:
1. Florida Institute of Technology , Melbourne , FL 32901 , USA
Abstract
Abstract
For a linear hyperbolic equation of fourth order, a Dirichlet type boundary problem in an orthogonally convex domain is investigated. Sharp sufficient conditions guaranteeing solvability and well-posedness of the problem under consideration are established.
Reference12 articles.
1. G. H. Hardy, J. E. Littlewood and G. Pólya,
Inequalities,
Cambridge Math. Libr.,
Cambridge University, Cambridge, 1988.
2. I. T. Kiguradze, Boundary value problems for systems of ordinary differential equations, Itogi Nauki Tekh. Ser. Sovrem. Probl. Mat. Noveishie Dostizh. 30 (1987), 3-103
3. translation in J. Sov.Math. 43 (1988), no. 2, 2259-2339.
4. T. Kiguradze,
Some boundary value problems for systems of linear partial differential equations of hyperbolic type,
Mem. Differential Equations Math. Phys. 1 (1994), 1–144.
5. T. Kiguradze,
On the correctness of the Dirichlet problem in a characteristic rectangle for fourth order linear hyperbolic equations,
Georgian Math. J. 6 (1999), no. 5, 447–470.