Spatial Structures in Geographical Economics Mathematical Modeling , Simulation and Inverse Problems

The Solow model is an economic model to describe economic growth. In this thesis we will provide an extension to this model by introducing a space dimension into the model and a production function that is non-concave. Furthermore, we will consider different kinds of technological progress. The resulting model is governed by a semilinear parabolic partial differential equation which describes the evolution of capital in time. We will consider the solution of the partial differential equation as our direct problem and show its well-posedness. Furthermore, we will present the numerical solution of this problem and examine the influence of the respective parameters on the model. We will then try to identify the production function in a situation where noisy data of the capital distribution over time is attainable. We will formulate the corresponding inverse problem, introduce a method to solve this inverse problem numerically and present some numerical results.