Date of Award
5-2025
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematics and Systems Engineering
First Advisor
Tariel Kiguradze
Second Advisor
Stanley Snelson
Third Advisor
Jian Du
Fourth Advisor
Pavithra Pathirathna
Abstract
Boundary value problems in a characteristic rectangle Ω = [0, ω1]×[0, ω2] for second order linear hyperbolic systems are considered.
For initial–boundary value problems 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–boundary value problems;
(vi) Necessary and sufficient conditions of solvability of ill–posed initial–periodic problems.
For nonlocal boundary value problems 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 boundary conditions of periodic type ;
(iv) Effective sufficient conditions of solvability of doubly–periodic problems;
(v) Necessary and sufficient conditions of solvability of ill–posed doubly–periodic problems.
Recommended Citation
Almutairi, Afrah, "Nonlocal Boundary Value Problems for Linear Hyperbolic Systems" (2025). Theses and Dissertations. 1563.
https://repository.fit.edu/etd/1563
