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This thesis is a mathematical investigation of damping effects in hyperbolic systems. In the first part two models from nonlinear acoustics are studied. Existence of time-periodic solutions to the Blackstock-Crighton equation and the Kuznetsov equation are established for time-periodic data sufficiently restricted in size. This leads to the conclusion that the dissipative effects in these models are sufficient to avoid resonance. In the second part the interaction of a viscous fluid with an elastic structure is studied. A periodic cell structure filled with a viscous fluid interacting with a deformable boundary of the cell is considered under time-periodic forcing. The motion of the fluid is governed by the Navier-Stokes equations and the deformable boundary is governed by the plate equation. It is shown that the damping mechanism induced by the viscous fluid is sufficient to avoid resonance in the elastic structure.
This book presents, in a methodical way, updated and comprehensive descriptions and analyses of some of the most relevant problems in the context of fluid-structure interaction (FSI). Generally speaking, FSI is among the most popular and intriguing problems in applied sciences and includes industrial as well as biological applications. Various fundamental aspects of FSI are addressed from different perspectives, with a focus on biomedical applications. More specifically, the book presents a mathematical analysis of basic questions like the well-posedness of the relevant initial and boundary value problems, as well as the modeling and the numerical simulation of a number of fundamental phenomena related to human biology. These latter research topics include blood flow in arteries and veins, blood coagulation and speech modeling. We believe that the variety of the topics discussed, along with the different approaches used to address and solve the corresponding problems, will help readers to develop a more holistic view of the latest findings on the subject, and of the relevant open questions. For the same reason we expect the book to become a trusted companion for researchers from diverse disciplines, such as mathematics, physics, mathematical biology, bioengineering and medicine.
We are interested in the time-asymptotic behavior of solutions to viscous conservation laws. Through the pointwise estimates for the Green's function of the linearized system and the analysis of coupling of nonlinear diffusion waves, we obtain explicit expressions of the time-asymptotic behavior of the solutions. This yields optimal estimates in the integral norms. For most physical models, the viscosity matrix is not positive definite and the system is hyperbolic-parabolic, and not uniformly parabolic. This implies that the Green's function may contain Dirac-functions. When the corresponding inviscid system is non-strictly hyperbolic, the time-asymptotic state contains generalized Burgers solutions. These are illustrated by applying our general theory to the compressible Navier-Stokes equations and the equations of magnetohydrodynamics.
Astronomy and Astrophysics Abstracts, which has appeared in semi-annual volumes since 1969, is devoted to the recording, summarizing and indexing of astronomical publications throughout the world. It is prepared under the auspices of the International Astronomical Union (according to a resolution adopted at the 14th General Assembly in 1970). Astronomy and Astrophysics Abstracts aims to present a comprehensive documenta tion of literature in all fields of astronomy and astrophysics. Every effort will be made to ensure that the average time interval between the date of receipt of the original literature and publication of the abstracts will not exceed eight months. This time interval is near to that achieved by monthly abstracting journals, compared to which our system of accumu lating abstracts for about six months offers the advantage of greater convenience for the user. Volume 32 contains literature published in 1982 and received before February 11, 1983; some older literature which was received late and which is not recorded in earlier volumes is also included. We acknowledge with thanks contributions to this volume by Dr. J. Bou~a, Prague, who surveyed journals and publications in Czech and supplied us with abstracts in English.