Date of Award
5-2025
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematical Sciences
First Advisor
Tariel Kiguradze
Second Advisor
Jewgani Dshalalow
Third Advisor
Jain Du
Fourth Advisor
Joo Young Park
Abstract
Title: Three-Dimensional Boundary Value Problems for Linear Hyperbolic Systems Author: Najma Alarbi Major Advisor: Dr. Tariel Kiguradze Initial–boundary value problems in a rectangular box Ω = [0, ω1] × [0, ω2] × [0, ω1] for linear hyperbolic systems are considered. For initial–boundary value problems with one–dimensional nonlocal conditions there are established: (i) Necessary and sufficient conditions of well–posedness; (ii) Necessary conditions of solvability; (iii) Effective sufficient conditions of solvability of two–point initial–boundary value problems; (iv) Effective sufficient conditions of solvability of initial–periodic problems; (v) Necessary and sufficient conditions of solvability of ill–posed initial–periodic problems. For initial–boundary value problems with two–dimensional nonlocal conditions there are established: (i) Necessary and sufficient conditions of well–posedness; (ii) Necessary conditions of solvability; (iii) Effective sufficient conditions of solvability of problems with Nicoletti type boundary conditions; (iv) Effective sufficient conditions of solvability of problems with doubly– periodic conditions; (v) Necessary and sufficient conditions of solvability of ill–posed problems with doubly–periodic conditions.
Recommended Citation
Alarbi, Najma, "Three-Dimensional Boundary Value Problem for Linear Hyperbolic System" (2025). Theses and Dissertations. 1531.
https://repository.fit.edu/etd/1531
