Stochastic Wave Propagation
Stochastic Wave Propagation

Author: K. Sobczyk

Publisher: Elsevier

Published: 2012-12-02

Total Pages: 257

ISBN-13: 0444598049

DOWNLOAD EBOOK

This is a concise, unified exposition of the existing methods of analysis of linear stochastic waves with particular reference to the most recent results. Both scalar and vector waves are considered. Principal attention is concentrated on wave propagation in stochastic media and wave scattering at stochastic surfaces. However, discussion extends also to various mathematical aspects of stochastic wave equations and problems of modelling stochastic media.

A Minicourse on Stochastic Partial Differential Equations
A Minicourse on Stochastic Partial Differential Equations

Author: Robert C. Dalang

Publisher: Springer Science & Business Media

Published: 2009

Total Pages: 230

ISBN-13: 3540859934

DOWNLOAD EBOOK

This title contains lectures that offer an introduction to modern topics in stochastic partial differential equations and bring together experts whose research is centered on the interface between Gaussian analysis, stochastic analysis, and stochastic PDEs.

Holder-Sobolev Regularity of the Solution to the Stochastic Wave Equation in Dimension Three
Holder-Sobolev Regularity of the Solution to the Stochastic Wave Equation in Dimension Three

Author: Robert C. Dalang

Publisher: American Mathematical Soc.

Published: 2009-04-10

Total Pages: 83

ISBN-13: 0821842889

DOWNLOAD EBOOK

The authors study the sample path regularity of the solution of a stochastic wave equation in spatial dimension $d=3$. The driving noise is white in time and with a spatially homogeneous covariance defined as a product of a Riesz kernel and a smooth function. The authors prove that at any fixed time, a.s., the sample paths in the spatial variable belong to certain fractional Sobolev spaces. In addition, for any fixed $x\in\mathbb{R}^3$, the sample paths in time are Holder continuous functions. Further, the authors obtain joint Holder continuity in the time and space variables. Their results rely on a detailed analysis of properties of the stochastic integral used in the rigourous formulation of the s.p.d.e., as introduced by Dalang and Mueller (2003). Sharp results on one- and two-dimensional space and time increments of generalized Riesz potentials are a crucial ingredient in the analysis of the problem. For spatial covariances given by Riesz kernels, the authors show that the Holder exponents that they obtain are optimal.

Stochastic Equations: Theory and Applications in Acoustics, Hydrodynamics, Magnetohydrodynamics, and Radiophysics, Volume 2
Stochastic Equations: Theory and Applications in Acoustics, Hydrodynamics, Magnetohydrodynamics, and Radiophysics, Volume 2

Author: Valery I. Klyatskin

Publisher: Springer

Published: 2014-07-14

Total Pages: 489

ISBN-13: 331907590X

DOWNLOAD EBOOK

In some cases, certain coherent structures can exist in stochastic dynamic systems almost in every particular realization of random parameters describing these systems. Dynamic localization in one-dimensional dynamic systems, vortexgenesis (vortex production) in hydrodynamic flows, and phenomenon of clustering of various fields in random media (i.e., appearance of small regions with enhanced content of the field against the nearly vanishing background of this field in the remaining portion of space) are examples of such structure formation. The general methodology presented in Volume 1 is used in Volume 2 Coherent Phenomena in Stochastic Dynamic Systems to expound the theory of these phenomena in some specific fields of stochastic science, among which are hydrodynamics, magnetohydrodynamics, acoustics, optics, and radiophysics. The material of this volume includes particle and field clustering in the cases of scalar (density field) and vector (magnetic field) passive tracers in a random velocity field, dynamic localization of plane waves in layered random media, as well as monochromatic wave propagation and caustic structure formation in random media in terms of the scalar parabolic equation.

Stochastic Wave Equations with Cubic Nonlinearities in Two Dimensions
Stochastic Wave Equations with Cubic Nonlinearities in Two Dimensions

Author: Haziem Mohammad Hazaimeh

Publisher:

Published: 2012

Total Pages: 288

ISBN-13:

DOWNLOAD EBOOK

The main focus of my dissertation is the qualitative and quantative behavior of stochastic Wave equations with cubic nonlinearities in two dimensions. The author evaluated the stochastic nonlinear wave equation in terms of its Fourier coecients. The author proved that the strong solution of that equation exists and is unique on an appropriate Hilbert space. Also, the author studied the stability of N -dimensional truncations and give conclusions in three cases: stability in probability, estimates of [Special characters omitted.] -growth, and almost sure exponential stability. The main tool is the study of related Lyapunov-type functionals which admits to control the total energy of randomly vibrating membranes. Finally, the author studied numerical methods for the Fourier coecients. The author focussed on the linear-implicit Euler method and the linear-implicit mid-point method. Their schemes have explicit representations. Eventually, the author investigated their mean consistency and mean square consistency.

Wave Phenomena
Wave Phenomena

Author: Willy Dörfler

Publisher: Springer Nature

Published: 2023-03-30

Total Pages: 368

ISBN-13: 3031057937

DOWNLOAD EBOOK

This book presents the notes from the seminar on wave phenomena given in 2019 at the Mathematical Research Center in Oberwolfach. The research on wave-type problems is a fascinating and emerging field in mathematical research with many challenging applications in sciences and engineering. Profound investigations on waves require a strong interaction of several mathematical disciplines including functional analysis, partial differential equations, mathematical modeling, mathematical physics, numerical analysis, and scientific computing. The goal of this book is to present a comprehensive introduction to the research on wave phenomena. Starting with basic models for acoustic, elastic, and electro-magnetic waves, topics such as the existence of solutions for linear and some nonlinear material laws, efficient discretizations and solution methods in space and time, and the application to inverse parameter identification problems are covered. The aim of this book is to intertwine analysis and numerical mathematics for wave-type problems promoting thus cooperative research projects in this field.