The Energy Method Stability And Nonlinear Convection

Six new chapters (14-19) deal with topics of current interest: multi-component convection diffusion, convection in a compressible fluid, convenction with temperature dependent viscosity and thermal conductivity, penetrative convection, nonlinear stability in ocean circulation models, and numerical solution of eigenvalue problems.

Emerging developments in nanofluid research have enhanced its range of various industrial applications. When implemented effectively, the use of such fluids offer numerous benefits, particularly in cooling processes. Nanofluid Technologies and Thermal Convection Techniques is a pivotal source of information for theoretical perspectives and investigations on the thermal instability of nanofluids and its various effects. Highlighting relevant studies relating to stationary, double diffusive, and oscillatory convection, this book is ideally designed for professionals, researchers, and practitioners seeking material on the industrial usage of nanofluid technologies.

This volume contains the proceedings of the Workshop Energy Methods for Free Boundary Problems in Continuum Mechanics, held in Oviedo, Spain, from March 21 to March 23, 1994. It is well known that the conservation laws and the constitutive equations of Continuum Mechanics lead to complicated coupled systems of partial differential equations to which, as a rule, one fails to apply the techniques usually employed in the studies of scalar uncoupled equations such as, for instance, the maximum principle. The study of the qualitative behaviour of solutions of the systems re quires different techniques, among others, the so called, Energy Methods where the properties of some integral of a nonnegative function of one or several unknowns allow one to arrive at important conclusions on the envolved unknowns. This vol ume presents the state of the art in such a technique. A special attention is paid to the class of Free Boundary Problems. The organizers are pleased to thank the European Science Foundation (Pro gram on Mathematical treatment of free boundary problems), the DGICYT (Spain), the FICYT (Principado de Asturias, Spain) and the Universities of Oviedo and Complutense de Madrid for their generous financial support. Finally, we wish to thank Kluwer Academic Publishers for the facilities received for the publication of these Proceedings.

This book contains recent contributions in the field of waves propagation and stability in continuous media. The volume is the sixth in a series published by World Scientific since 1999.

For the past several decades, the study of free boundary problems has been a very active subject of research occurring in a variety of applied sciences. What these problems have in common is their formulation in terms of suitably posed initial and boundary value problems for nonlinear partial differential equations. Such problems arise, for example, in the mathematical treatment of the processes of heat conduction, filtration through porous media, flows of non-Newtonian fluids, boundary layers, chemical reactions, semiconductors, and so on. The growing interest in these problems is reflected by the series of meetings held under the title "Free Boundary Problems: Theory and Applications" (Ox ford 1974, Pavia 1979, Durham 1978, Montecatini 1981, Maubuisson 1984, Irsee 1987, Montreal 1990, Toledo 1993, Zakopane 1995, Crete 1997, Chiba 1999). From the proceedings of these meetings, we can learn about the different kinds of mathematical areas that fall within the scope of free boundary problems. It is worth mentioning that the European Science Foundation supported a vast research project on free boundary problems from 1993 until 1999. The recent creation of the specialized journal Interfaces and Free Boundaries: Modeling, Analysis and Computation gives us an idea of the vitality of the subject and its present state of development. This book is a result of collaboration among the authors over the last 15 years.

The topics covered include soil mechanics and porous media, glacier and ice dynamics, climatology and lake physics, climate change as well as numerical algorithms. The book, written by well-known experts, addresses researchers and students interested in physical aspects of our environment.

Herbert Amann's work is distinguished and marked by great lucidity and deep mathematical understanding. The present collection of 31 research papers, written by highly distinguished and accomplished mathematicians, reflect his interest and lasting influence in various fields of analysis such as degree and fixed point theory, nonlinear elliptic boundary value problems, abstract evolutions equations, quasi-linear parabolic systems, fluid dynamics, Fourier analysis, and the theory of function spaces. Contributors are A. Ambrosetti, S. Angenent, W. Arendt, M. Badiale, T. Bartsch, Ph. Bénilan, Ph. Clément, E. Faöangová, M. Fila, D. de Figueiredo, G. Gripenberg, G. Da Prato, E.N. Dancer, D. Daners, E. DiBenedetto, D.J. Diller, J. Escher, G.P. Galdi, Y. Giga, T. Hagen, D.D. Hai, M. Hieber, H. Hofer, C. Imbusch, K. Ito, P. Krejcí, S.-O. Londen, A. Lunardi, T. Miyakawa, P. Quittner, J. Prüss, V.V. Pukhnachov, P.J. Rabier, P.H. Rabinowitz, M. Renardy, B. Scarpellini, B.J. Schmitt, K. Schmitt, G. Simonett, H. Sohr, V.A. Solonnikov, J. Sprekels, M. Struwe, H. Triebel, W. von Wahl, M. Wiegner, K. Wysocki, E. Zehnder and S. Zheng.

Mathematical problems concerning time evolution of solutions related to nonlinear systems modelling dynamics of continuous media are of great interest both in wave propagation and in stability problems. During the last few decades many striking developments have taken place, especially in connection with the effects of nonlinearity of the equations describing physical situations. The articles in this book have been written by reputable specialists in the field and represent a valuable contribution to its advancement. The topics are: discontinuity and shock waves; linear and nonlinear stability in fluid dynamics; kinetic theories and comparison with continuum models; propagation and non-equilibrium thermodynamics; exact solutions via group methods; numerical applications.

The book contains recent contributions in the field of waves propagation and stability in continuous media. In particular, the contributions consider discontinuity and shock waves, stability in fluid dynamics, small parameter problems, kinetic theories towards continuum models, non-equilibrium thermodynamics, and numerical applications.The volume is the fourth in a series published by World Scientific since 1999. The following distinguished authors contribute to the present book: S Bianchini, R Caflish, C Cercignani, Y Choquet-Bruhat, C Dafermos, L Desvillettes, V Giovangigli, H Gouin, I Muller, D Parker, B Straughan, M Sugiyama and W Weiss.