Date of Award
5-2017
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematical Sciences
First Advisor
Tariel Kiguradze
Second Advisor
Jay Kovats
Third Advisor
Muzaffar Shaikh
Fourth Advisor
Gnana Bhaskar Tenali
Abstract
Boundary value problems in a characteristic rectangle for nonlinear hyperbolic equations of higher order 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 two–point, multi–point, periodic and Dirichlet type problems; (iv) Sharp a priori estimates of solutions of ill–posed initial–boundary value problems; (v) Unimprovable conditions guaranteeing unique solvability of ill–posed initial–boundary value problems. For nonlocal boundary value problems there are established: (i) Necessary and sufficient conditions for a linear problem to have the Fredholm property; (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 periodic and Dirichlet type problems in case, where the righthand side of the equation has arbitrary growth order with respect to some phase variables.
Recommended Citation
Ben-Rabha, Raja, "Initial{Boundary and Nonlocal Boundary Value Problems for Higher Order Nonlinear Hyperbolic Equations with Two Independent Variables" (2017). Theses and Dissertations. 941.
https://repository.fit.edu/etd/941