Qualitative Properties of Dispersive PDEs (eBook)

This book provides a valuable collection of contributions by distinguished scholars presenting the state of the art and some of the most significant latest developments and future challenges in the field of dispersive partial differential equations. The material covers four major lines: (1) Long time behaviour of NLS-type equations, (2) probabilistic and nonstandard methods in the study of NLS equation, (3) dispersive properties for heat-, Schrödinger-, and Dirac-type flows, (4) wave and KdV-type equations. Across a variety of applications an amount of crucial mathematical tools are discussed, whose applicability and versatility goes beyond the specific models presented here. Furthermore, all contributions include updated and comparative literature.

Vladimir Georgiev is a former Alexander von Humboldt fellow. He is a Full Professor of mathematics at the University of Pisa. The main fields of the research interests involve decay estimates for equations of Mathematical Physics on flat or curved space - time, smoothing and Strichartz estimates for evolution problems, global existence of small and large data solutions to equations of classical quantum mechanics, existence and stability of solitary waves, Maxwell-Dirac and Maxwell-Scrödinger equation, scattering and long range effects for relativistic and non - relativistic particles and fields.

Alessandro Michelangeli is an Alexander von Humboldt Senior Researcher at the Institute for Applied Mathematics and at the Hausdorff Center for Mathematics, Bonn, and a member of the Institute of Theoretical Quantum Technologies Trieste. He also held positions at the LMU Munich and the SISSA Trieste. His research is at the interface of analysis, mathematical physics, and theoretical physics, with expertise in functional analysis, operator theory, spectral theory, non-linear partial differential equations, and quantum mechanics.

Raffaele Scandone is a postdoctoral researcher at Gran Sasso Science Institute, Italy. He received his PhD in Mathematics at SISSA, Italy, in 2014. His research interests lie in the area of dispersive PDEs, with a particular focus on Schrodinger-type equations and quantum hydrodynamics.

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This book provides a valuable collection of contributions by distinguished scholars presenting the state of the art and some of the most significant latest developments and future challenges in the field of dispersive partial differential equations. The material covers four major lines: (1) Long time behaviour of NLS-type equations, (2) probabilistic and nonstandard methods in the study of NLS equation, (3) dispersive properties for heat-, Schrodinger-, and Dirac-type flows, (4) wave and KdV-type equations. Across a variety of applications an amount of crucial mathematical tools are discussed, whose applicability and versatility goes beyond the specific models presented here. Furthermore, all contributions include updated and comparative literature.