| In this dissertation, we deal with Maxwell's equations coupled with a nonlinear heat equation. Throughout this dissertation, I refer [13] many times.; In Chapter 1, we derive Maxwell's equations and heat equation.; In Chapter 2, we introduce some function spaces which are used in this dissertation.; In Chapter 3, we prove well-posedness of Maxwell's system only. We do not consider temperature effect yet. First, we define weak solution of Maxwell's system. Maxwell's system is a coupled of first order partial differential equations. By introducing new function, we change Maxwell's system to second order single partial differential equation. We define weak solution of alternative form of Maxwell's system. We prove existence and uniqueness of alternative form of Maxwell's system.; In Chapter 4, we prove existence of Maxwell's system with temperature effect. First, we define weak solution of heat equation. In Chapter 3, we know the existence and uniqueness of Maxwell's system. With that solution, we prove the existence of Maxwell's system with temperature effect by using Schauder fixed point theorem.; In Chapter 5, we consider spacial case which is one space dimension. By using energy method, we prove the existence of classical solution. |
