http://localhost:8081/jspui/handle/123456789/120 2026-04-19T19:13:14Z 2026-04-19T19:13:14Z Handa, Ajay http://localhost:8081/jspui/handle/123456789/19114 2026-02-20T06:43:00Z 2021-06-01T00:00:00Z

Title: AN INTRODUCTION TO MATHEMATICAL OPTIMAL CONTROL THEORY Authors: Handa, Ajay Abstract: In control theory, we are interested in governing the state of a system by using controls. One can explain Optimal Control Theory as the science of maximizing the returns and minimizing the costs of the operation of physical, social, and economic processes. In this work, we are devoted to study the controllability and the existence of optimal control of linear first order ordinary differential equations. And then, we study the Pontryagin Maximum Principle which helps us to characterize the optimal control. In this work, our main aim is to study the existence of optimal control, the Pontryagin Maximum Principle and its various applications.

2021-06-01T00:00:00Z Manik, Tripti http://localhost:8081/jspui/handle/123456789/19051 2026-02-16T10:45:44Z 2024-04-01T00:00:00Z

Title: SEMIGROUP THEORY AND EVOLUTION EQUATIONS Authors: Manik, Tripti Abstract: The present dissertation provides information about the fundamental concepts of Semigroup Theory and its applications to differential equations (Cauchy problem). In this project, the basis for our study is the evolution equation. When we solve a Cauchy problem we get a family of evolution operators that can take the starting condition of a system and predict its state at a later time that means solving the Cauchy problem is the same as finding a family of evolution operators E(t) and the properties which operator E(t) satisfies are called the semigroup properties. The study begins with a comprehensive review of the basic definitions and properties of semigroups, the project delves into the classification of semigroups based on various structural properties and algebraic operations. Here special attention is given to the classification of semigroups such as Uniformly continuous semigroups, Strongly continuous semigroups, Contraction semigroups, and some key concepts of these semigroups like generator, resolvent, infinitesimal generators, etc. Here we study the Hille-Yosida Theorem and Lumer-Phillips Theorem which emerge as a powerful tool for understanding the structure and complexity of Contraction semigroup. We also study the application of semigroup in various areas of PDEs such as Heat equation, transport equation, etc. The dissertation concludes with reflections on semigroups, their properties, and applications.

2024-04-01T00:00:00Z Datta, Swarnali http://localhost:8081/jspui/handle/123456789/19050 2026-02-16T10:45:35Z 2024-05-01T00:00:00Z

Title: ALGEBRAIC THEORY OF DIFFERENTIAL EQUATIONS Authors: Datta, Swarnali Abstract: My project topic explains how to look a polynomial coefficient linear differential equations in an algebraic environment. While differential equations are commonly considered to belong to the world of analysis, algebra has a lot of interesting things to say about differential equations and their solutions. The algebraic theory of linear differential equations serves as an analogue to ”The classical Galois theory for polynomial equations”. In this context, a differential field, comprising a field F (having characteristic 0) equipped with a derivation akin to the differentiation in R or C, plays a central role. So basically differentiation can be seen as a homomorphism point of view and consequently we can apply algebraic properties on differentiation.

2024-05-01T00:00:00Z Sharma, Sushil http://localhost:8081/jspui/handle/123456789/19049 2026-02-16T10:45:08Z 2024-04-01T00:00:00Z

Title: UNVEILING THE COMPLEXITIES OF PREDATOR-PREY INTERACTIONS: A SPATIO TEMPORAL APPROACH Authors: Sharma, Sushil Abstract: This project immerses itself in the captivating realm of predator-prey interactions, employing mathematical modeling as a powerful tool to dissect and comprehend the underlying dynamics. Through a meticulously structured approach, it unfolds three comprehensive investigations, each meticulously crafted to illuminate the nuanced interplay governing these populations. By delving deep into the intricacies of predator-prey relationships, this study endeavors to unravel the complex web of interactions, offering valuable insights into the mechanisms shaping ecosystem dynamics.

2024-04-01T00:00:00Z