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