Existence and stability analysis for non-autonomous systems of differential equations in multi-dimensional time

Author

Michael Lott Jr.

Date of Award

2025

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematical Sciences

Committee Chair

Toka Diagana

Committee Member

Claudio Morales

Committee Member

Shangbing Ai

Committee Member

Milena Stanislavova

Committee Member

Yuanzhen Shao

Research Advisor

Toka Diagana

Subject(s)

Evolution equations, Functional analysis, Banach spaces

Abstract

This dissertation studies the existence and stability of solutions for a class of non-autonomous systems of differential equations in multi-dimensional time, within the framework of Banach space. Focusing on both hyperbolic and parabolic cases, it presents a comprehensive range of results on existence and stability over finite and infinite time intervals. By leveraging the theory of evolution families, this work uncovers the conditions under which these systems have solutions and provides an in-depth analysis of how these solutions evolve, offering fresh perspectives on their dynamic behavior over time.

Comments

Submitted ... in the joint Applied Mathematics Program.

Recommended Citation

Lott, Michael Jr., "Existence and stability analysis for non-autonomous systems of differential equations in multi-dimensional time" (2025). Dissertations. 443.
https://louis.uah.edu/uah-dissertations/443