Applied Partial Differential Equations

This book presents topics of science and engineering occuring in nature and/or are part of our daily lives. The described natural/engineering phenomena are modelled 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 topics chosen in the book, which reflect the longtime scientific interests of the author are briefly presented in their scientific or engineering context and then the mathematical models in the form of partial differential equations are introduced and their basic mathematical properties are discussed. The author illustrates each chapter by a series of high quality photographs demonstrating that partial differential equations can be used for a large variety of phenomena. TOC:Fluid and Gas Dynamics Granular Gas Dynamics Chemotaxis and Pattern Formation in Animals Reaction-Diffusion Equations – Structured Environments Kinetics of Rarified Gases: The Boltzmann Equation Semiconductor Modelling Optimal Transport and Monge-Ampere Equations Wave Equations Digital Image Processing and Analysis Partial Differential Equations in Glacier Physics Free Boundaries and Interfaces: the Stefan Problem