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Foreword
VI

images were acquired using digital cameras, among them a Nikon D100, Nikon
D2x, Nikon D200, Kodak 14nx, Hasselblad H1 with a PhaseOne P25/45 digital
backs. I always choose the RAW format for digital image acqusition, process the
images first in a RAW converter and then do the necessary post-processing in
Photoshop CS2.
The photographs are here for enjoyment but also – and more importantly
in a scientific context – they shall convey a message: applied mathematics,
particularly partial differential equation modeling, is useful for a wide range
of problems and applications originating from the nature which surrounds us,
from socio-economics and from technological applications.
So much about the photographs, but what can be said about the math? Ac-
tually, the choice of the topics Chapter 1 to Chapter 11 was mainly decided
by my own research background and expertise, ‘completeness’ was never in-
tended nor can it be achieved. The depth and style of the mathematical pre-
sentation is supposed to be such that everybody with a solid knowledge of
multi-dimensional calculus can understand the text. In particular, students and
researchers interested in modeling with partial differential equations are a clear
target group of this book. But also, analytically or numerically oriented re-
searchers in partial differential equations who are interested in new applications
will hopefully get something out. Then, of course, the material of this book is
accessible to engineers, physicists and other scientists with a basic mathematical
education.
I have taken mathematical inspiration from many people. In particular
I want to mention my dear friend Frédéric Poupaud, who passed away in
the year 2004. Then my former students and friends Anton Arnold, Ans-
gar Jüngel, Ingo Gasser, Norbert Mauser and Christof Sparber, my colleagues
and friends Christian Schmeiser, Christian Ringhofer, Andreas Unterreiter,
Franco Brezzi, Giuseppe Toscani, Luis Caffarelli, Norayr Matevosyan, Irene
Gamba, Pierre Degond, Naoufel Ben Abdallah, Henrik Shagholian, Benoit
Perthame, Yann Brenier, Claude Bardos, David Levermore, Patrick Gerard,
Paola Pietra, Martin Burger, Lorenzo Pareschi, Shi Jin, Weizhu Bao, Kazuo
Aoki, Ester Gabetta, Claudia Lederman, Jorge Zubelli, Antonio Leitao, Heinz
Engl, Jose Carrillo, Juan-Luis Vazquez and Cedric Villani. In particular I thank
Giuseppe Toscani and Dietmar Ölz for coauthoring Chapters of this book
with me.
My special gratitude goes to my friend and Administrator of my research
grants, Renate Feikes, for friendship and many organisational miracles, to An-
drea Baczynski, forloveand photographic advice andtomydaughterAnnafor
sitting (suffering …) through some of my talks at various conferences all over
the world.
I acknowledge funding of my research over the past five years from the
Austrian Research Fund FWF through my Wittgenstein Award 2000 (financed
by the Austrian Ministry for Education, Science and Culture), from the EC