Date of Award

12-2023

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics and Systems Engineering

First Advisor

Tariel Kiguradze

Second Advisor

Jay Kovats

Third Advisor

Micheal Shaw

Fourth Advisor

Ryan Stansifer

Abstract

Boundary value problems in a characteristic rectangle Ω = [0, ω1] × [0, ω2] for second order quasi-linear hyperbolic systems are considered. The concept of strong well– posedness of a boundary value problem is introduced. For initial–boundary value problems there are established: (i) Necessary and sufficient conditions of strong well–posedness; (ii) Unimprovable sufficient conditions of local and global solvability; (iii) Effective sufficient conditions of solvability of Nicoletti type two–point initial– boundary value problems in case, where the righthand side of the system has arbitrary growth order in some phase variables. For nonlocal boundary value problems there are established: (i) Necessary conditions of solvability; (ii) Necessary and sufficient conditions of strong well–posedness; (iii) Optimal sufficient conditions of solvability and unique solvability; (iv) Effective sufficient conditions of solvability of Nicoletti type two–point boundary value problems in case, where the righthand side of the system has arbitrary growth order in some phase variables.

Comments

Copyright held by author.

Available for download on Tuesday, December 16, 2025

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