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.

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