Burgers-KPZ Turbulence [electronic resource] : Göttingen Lectures / by Wojbor A. Woyczyński.
Material type: TextSeries: Lecture Notes in Mathematics ; 1700Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 1998Description: XII, 328 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783540494805Subject(s): Mathematics | Differential equations, partial | Distribution (Probability theory) | Mathematics | Partial Differential Equations | Probability Theory and Stochastic ProcessesAdditional physical formats: Printed edition:: No titleDDC classification: 515.353 LOC classification: QA370-380Online resources: Click here to access onlineCurrent library | Home library | Call number | Materials specified | URL | Status | Date due | Barcode |
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IMSc Library | IMSc Library | Link to resource | Available | EBK1752 |
Shock waves and the large scale structure (LSS) of the universe -- Hydrodynamic limits, nonlinear diffusions, and propagation of chaos -- Hopf-Cole formula and its asymptotic analysis -- Statistical description, parabolic approximation -- Hyperbolic approximation and inviscid limit -- Forced Burgers turbulence -- Passive tracer transport in Burgers' and related flows -- Fractal Burgers-KPZ models.
These lecture notes are woven around the subject of Burgers' turbulence/KPZ model of interface growth, a study of the nonlinear parabolic equation with random initial data. The analysis is conducted mostly in the space-time domain, with less attention paid to the frequency-domain picture. However, the bibliography contains a more complete information about other directions in the field which over the last decade enjoyed a vigorous expansion. The notes are addressed to a diverse audience, including mathematicians, statisticians, physicists, fluid dynamicists and engineers, and contain both rigorous and heuristic arguments. Because of the multidisciplinary audience, the notes also include a concise exposition of some classical topics in probability theory, such as Brownian motion, Wiener polynomial chaos, etc.
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