Gubinelli / Souganidis / Tzvetkov Singular Random Dynamics

Cetraro, Italy 2016
Erscheinungsjahr 2019
ISBN: 978-3-030-29545-5
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 2253, 316 Seiten, eBook

Reihe: Lecture Notes in Mathematics

Written by leading experts in an emerging field, this book offers a unique view of the theory of stochastic partial differential equations, with lectures on the stationary KPZ equation, fully nonlinear SPDEs, and random data wave equations. This subject has recently attracted a great deal of attention, partly as a consequence of Martin Hairer's contributions and in particular his creation of a theory of regularity structures for SPDEs, for which he was awarded the Fields Medal in 2014. The text comprises three lectures covering: the theory of stochastic Hamilton–Jacobi equations, one of the most intriguing and rich new chapters of this subject; singular SPDEs, which are at the cutting edge of innovation in the field following the breakthroughs of regularity structures and related theories, with the KPZ equation as a central example; and the study of dispersive equations with random initial conditions, which gives new insights into classical problems and at the same timeprovides a surprising parallel to the theory of singular SPDEs, viewed from many different perspectives. These notes are aimed at graduate students and researchers who want to familiarize themselves with this new field, which lies at the interface between analysis and probability.

Zielgruppe

Research

Autoren/Hrsg.

Gubinelli, Massimiliano

Souganidis, Panagiotis E.

Tzvetkov, Nikolay

Flandoli, Franco

Hairer, Martin

Inhaltsverzeichnis

- Introduction. - Lectures on Energy Solutions for the Stationary KPZ Equation. - Pathwise Solutions for Fully Nonlinear First- and Second-Order Partial Differential Equations with Multiplicative Rough Time Dependence. - Random Data Wave Equations.