Lecture Notes in Mathematics
3 primary works
Book 1855
Functional Analytic Methods for Evolution Equations
by Giuseppe Da Prato, Peer Christian Kunstmann, Irena Lasiecka, Alessandra Lunardi, Roland Schnaubelt, and Lutz Weis
This book consists of five introductory contributions by leading mathematicians on the functional analytic treatment of evolutions equations. In particular the contributions deal with Markov semigroups, maximal L^p-regularity, optimal control problems for boundary and point control systems, parabolic moving boundary problems and parabolic nonautonomous evolution equations. The book is addressed to PhD students, young researchers and mathematicians doing research in one of the above topics.
Book 1905
A Concise Course on Stochastic Partial Differential Equations
by Claudia Prevot and Michael Roeckner
These lectures concentrate on (nonlinear) stochastic partial differential equations (SPDE) of evolutionary type. There are three approaches to analyze SPDE: the "martingale measure approach", the "mild solution approach" and the "variational approach". The purpose of these notes is to give a concise and as self-contained as possible an introduction to the "variational approach". A large part of necessary background material is included in appendices.
Book 2163
Stochastic Porous Media Equations
by Viorel Barbu, Giuseppe Da Prato, and Michael Roeckner
The porous media equation models a number of different physical phenomena, including the flow of an ideal gas and the diffusion of a compressible fluid through porous media, and also thermal propagation in plasma and plasma radiation. Another important application is to a model of the standard self-organized criticality process, called the "sand-pile model" or the "Bak-Tang-Wiesenfeld model".
The book will be of interest to PhD students and researchers in mathematics, physics and biology.