Applied Partial Differential Equations:

This book presents topics of science and engineering which occur in nature or are part of our daily lives. The described natural or engineering phenomena are modeled by partial differential equations, which relate physical variables like mass, velocity, energy, etc. to their spatial and temporal variations. Typically these equations are highly nonlinear, in many cases they are also vectorial systems, and they represent a challenge even for the most modern and sophisticated mathematical-analytical and mathematical-numerical techniques. The chosen topics reflect the longtime scientific interests of the author. They include flows of fluids and gases, granular material flows, biological processes like pattern formation on animal skins, kinetics of rarified gases and semiconductor devices. Each topic is briefly introduced in its scientific or engineering context, followed by a presentation of the mathematical models in the form of partial differential equations with a discussion of their basic mathematical properties. The author illustrates each chapter by a series of his own high-quality photographs demonstrating that partial differential equations can be used to model a large variety of phenomena occurring in and influencing our daily lives.