Date of Award
5-2022
Document Type
Dissertation
Degree Name
Master of Science (MS)
Department
Mathematical Sciences
First Advisor
Tariel Kiguradze
Second Advisor
Ryan Stansifer
Third Advisor
Kanishka Perera
Fourth Advisor
Jian Du
Abstract
Dirichlet type problems for quasi-linear hyperbolic equations are considered. For two-dimensional boundary value problems there are established:
(i) Unimprovable sufficient conditions of unique solvability and well-posedness of linear problems in piecewise smooth domains;
(ii) Unimprovable Sufficient conditions of unique solvability of linear problems in smooth convex domains.
(iii) Optimal Sufficient conditions of solvability, unique solvability and strong well-posedness of quasi-linear problems in piecewise smooth domains;
(iv) Optimal sufficient conditions of solvability and unique solvability of quasi- linear problems in smooth convex domains.
For three-dimensional linear boundary value problems there are established:
(i) Unimprovable sufficient conditions of unique solvability and well-posedness of linear problems in cylindrical domains with a piecewise smooth base;
(ii) Unimprovable Sufficient conditions of unique solvability of linear problems in cylindrical domains with a smooth base;
(iii) Optimal Sufficient conditions of solvability and unique solvability of quasi- linear problems in cylindrical domains with a piecewise smooth base;
(iv) Optimal suffcient conditions of solvability and unique solvability of quasi- linear problems in cylindrical domains with a smooth base.
Recommended Citation
Alhuzally, Reemah, "Dirichlet Type Boundary Value Problems for Linear and Quasi{Linear Hyperbolic Equations of Higher Order" (2022). Theses and Dissertations. 1347.
https://repository.fit.edu/etd/1347
Comments
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