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In this monograph, the authors develop a comprehensive approach for
the mathematical analysis of a wide array of problems involving
moving interfaces. It includes an in-depth study of abstract
quasilinear parabolic evolution equations, elliptic and parabolic
boundary value problems, transmission problems, one- and two-phase
Stokes problems, and the equations of incompressible viscous one-
and two-phase fluid flows. The theory of maximal regularity, an
essential element, is also fully developed. The authors present a
modern approach based on powerful tools in classical analysis,
functional analysis, and vector-valued harmonic analysis. The
theory is applied to problems in two-phase fluid dynamics and phase
transitions, one-phase generalized Newtonian fluids, nematic liquid
crystal flows, Maxwell-Stefan diffusion, and a variety of geometric
evolution equations. The book also includes a discussion of the
underlying physical and thermodynamic principles governing the
equations of fluid flows and phase transitions, and an exposition
of the geometry of moving hypersurfaces.
In this monograph, the authors develop a comprehensive approach for
the mathematical analysis of a wide array of problems involving
moving interfaces. It includes an in-depth study of abstract
quasilinear parabolic evolution equations, elliptic and parabolic
boundary value problems, transmission problems, one- and two-phase
Stokes problems, and the equations of incompressible viscous one-
and two-phase fluid flows. The theory of maximal regularity, an
essential element, is also fully developed. The authors present a
modern approach based on powerful tools in classical analysis,
functional analysis, and vector-valued harmonic analysis. The
theory is applied to problems in two-phase fluid dynamics and phase
transitions, one-phase generalized Newtonian fluids, nematic liquid
crystal flows, Maxwell-Stefan diffusion, and a variety of geometric
evolution equations. The book also includes a discussion of the
underlying physical and thermodynamic principles governing the
equations of fluid flows and phase transitions, and an exposition
of the geometry of moving hypersurfaces.
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.
Benilan, Ph. Clement, E. Faoangova, 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. Krejci, S.-O. Londen, A.
Lunardi, T. Miyakawa, P. Quittner, J. Pruss, 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.
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.
BA(c)nilan, Ph. ClA(c)ment, E. FaAangovA, 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. KrejcA-,
S.-O. Londen, A. Lunardi, T. Miyakawa, P. Quittner, J. PrA1/4ss,
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.
The volume originates from the 'Conference on Nonlinear Parabolic
Problems' held in celebration of Herbert Amann's 70th birthday at
the Banach Center in Bedlewo, Poland. It features a collection of
peer-reviewed research papers by recognized experts highlighting
recent advances in fields of Herbert Amann's interest such as
nonlinear evolution equations, fluid dynamics, quasi-linear
parabolic equations and systems, functional analysis, and more.
Mathematical Models in Medical and Health Science is composed of
refereed and carefully edited research articles derived from the
Conference on Mathematical Models in Medical and Health Sciences,
held at Vanderbilt University in conjunction with the thirteenth
annual Shanks Lectures Series, May 1997. As did the conference,
this innovative volume brings together mathematicians, biologists,
and medical researchers in a forum that promotes their
interdisciplinary cooperation.
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