Stochastic Partial Differential Equations: An Introduction

Motivation, Aims and Examples.- Stochastic Integral in Hilbert Spaces.- SDEs in Finite Dimensions.- SDEs in Infinite Dimensions and Applications to SPDEs.- SPDEs with Locally Monotone Coefficients.- Mild Solutions.

Wei Liu is currently Jiangsu Specially-Appointed Professor of Mathematics at Jiangsu Normal University. He holds a PhD from University of Bielefeld.

Michael Rockner has held positions at the Universities of Edinburgh and Bonn, as well as Purdue University. He is currently Professor of Mathematics at Bielefeld University.

Michael Röckner has held positions at the Universities of Edinburgh and Bonn, as well as Purdue University. He is currently Professor of Mathematics at Bielefeld University. His main fields of research are in Probability Theory and Analysis, especially in Stochastic Analysis. He has made various contributions to these fields, in particular to the Theory of Dirichlet Forms and Markov Processes, to Fokker-Planck-Kolmogorov Equations and to Stochastic Partial Differential Equations (SPDEs). Among his main interests are, furthermore, applications to problems in Mathematical Physics. He is a coauthor of about 250 publications in scientific journals, 4 books and one Springer Lecture Notes in Mathematics. In the past few years jointly with Wei Liu he developed an extended variational approach to SPDEs, relaxing the usual monotonicity and coercivity conditions, also allowing explosion of solutions in finite time. This leads to a unifying systematic framework covering a large class of classical, but also new types of SPDEs.