From L?vy-Type Processes to Parabolic SPDEs, Davar Khoshnevisan; Ren? Schilling; Frederic Utzet

Автор: Oscar E. Lanford III; Michael Yampolsky
Название: Fixed Point of the Parabolic Renormalization Operator
ISBN: 3319117068 ISBN-13(EAN): 9783319117065
Издательство: Springer
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Цена: 46570.00 T
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This monograph grew out of the authors' efforts to provide a natural geometric description for the class of maps invariant under parabolic renormalization and for the Inou-Shishikura fixed point itself as well as to carry out a computer-assisted study of the parabolic renormalization operator. It introduces a renormalization-invariant class of analytic maps with a maximal domain of analyticity and rigid covering properties and presents a numerical scheme for computing parabolic renormalization of a germ, which is used to compute the Inou-Shishikura renormalization fixed point.

Inside, readers will find a detailed introduction into the theory of parabolic bifurcation, Fatou coordinates, calle-Voronin conjugacy invariants of parabolic germs, and the definition and basic properties of parabolic renormalization.

The systematic view of parabolic renormalization developed in the book and the numerical approach to its study will be interesting to both experts in the field as well as graduate students wishing to explore one of the frontiers of modern complex dynamics.

Автор: K?nig
Название: The Parabolic Anderson Model
ISBN: 3319335952 ISBN-13(EAN): 9783319335957
Издательство: Springer
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Цена: 71730.00 T
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Описание: This is a comprehensive survey on the research on the parabolic Andersonmodel – the heat equation with random potential or the random walk in randompotential – of the years 1990 – 2015. The investigation of this model requiresa combination of tools from probability (large deviations, extreme-valuetheory, e.g.) and analysis (spectral theory for the Laplace operator withpotential, variational analysis, e.g.). We explain the background, theapplications, the questions and the connections with other models and formulatethe most relevant results on the long-time behavior of the solution, like quenchedand annealed asymptotics for the total mass, intermittency, confinement andconcentration properties and mass flow. Furthermore, we explain the mostsuccessful proof methods and give a list of open research problems. Proofs arenot detailed, but concisely outlined and commented; the formulations of sometheorems are slightly simplified for better comprehension.

Автор: Atsushi Yagi
Название: Abstract Parabolic Evolution Equations and their Applications
ISBN: 3642261795 ISBN-13(EAN): 9783642261794
Издательство: Springer
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Цена: 102480.00 T
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Описание: This book offers an overview of the theories of linear, semilinear and quasilinear abstract parabolic evolution equations. It also shows how to apply the abstract results to various models in the real world focusing on various self-organization models.

Название: Parabolic Equations in Biology
ISBN: 3319194992 ISBN-13(EAN): 9783319194998
Издательство: Springer
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Цена: 37270.00 T
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Описание: This book presents several fundamental questions in mathematical biology such as Turing instability, pattern formation, reaction-diffusion systems, invasion waves and Fokker-Planck equations.

Автор: Sergio Albeverio; Giuseppe Da Prato; Franco Flando
Название: SPDE in Hydrodynamics: Recent Progress and Prospects
ISBN: 3540784926 ISBN-13(EAN): 9783540784920
Издательство: Springer
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Цена: 32560.00 T
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Описание: Reflects on the three lecture courses making up the CIME summer school on Fluid Dynamics at Cetraro in 2005. This title describes deterministic and stochastic models of hydrodynamics. It also describes rigorous mathematical results for multidimensional Navier-Stokes systems.