Blowup in the Complex Ginzburg-Landau Equation

In this thesis, we study the stability of a finite-time blowup solution of a partial di erential equation (PDE). Partial di erential equations can be used to model phenomena in a wide range of applications. Examples of well known partial di erential equations are: the heat equation which models heat conduction in a medium; the Navier-Stokes equation which describes the motion of fluids; and (a system of coupled nonlinear) reaction-di usion equations which model(s) the density of for example chemical substances that can undergo a reaction. In initial value problems (also called Cauchy problems), an initial state at t = 0 and boundary conditions are specified. And, if local existence and uniqueness of solutions is established, the aim of initial value problems is to solve these equations and thereby determine the state, depending on space, for t > 0. A priori, it is, however, not clear that through solving the equation it is possible to determine the state for all t > 0.