Global Well-posedness of Nonlinear Parabolic-Hyperbolic Coupled Systems

Global Well-posedness of Nonlinear Parabolic-Hyperbolic Coupled Systems
Author: Yuming Qin
Publisher: Springer Science & Business Media
Total Pages: 181
Release: 2012-02-28
Genre: Mathematics
ISBN: 3034802803

This book presents recent results on nonlinear parabolic-hyperbolic coupled systems such as the compressible Navier-Stokes equations, and liquid crystal system. It summarizes recently published research by the authors and their collaborators, but also includes new and unpublished material. All models under consideration are built on compressible equations and liquid crystal systems. This type of partial differential equations arises not only in many fields of mathematics, but also in other branches of science such as physics, fluid dynamics and material science.

Nonlinear Parabolic-Hyperbolic Coupled Systems and Their Attractors

Nonlinear Parabolic-Hyperbolic Coupled Systems and Their Attractors
Author: Yuming Qin
Publisher: Springer Science & Business Media
Total Pages: 472
Release: 2008-11-25
Genre: Mathematics
ISBN: 3764388145

This book presents recent results concerning the global existence in time, the large-time behavior, decays of solutions and the existence of global attractors for nonlinear parabolic-hyperbolic coupled systems of evolutionary partial differential equations.

Global Well-posedness and Asymptotic Behavior of the Solutions to Non-classical Thermo(visco)elastic Models

Global Well-posedness and Asymptotic Behavior of the Solutions to Non-classical Thermo(visco)elastic Models
Author: Yuming Qin
Publisher: Springer
Total Pages: 206
Release: 2016-07-29
Genre: Mathematics
ISBN: 981101714X

This book presents recent findings on the global existence, the uniqueness and the large-time behavior of global solutions of thermo(vis)coelastic systems and related models arising in physics, mechanics and materials science such as thermoviscoelastic systems, thermoelastic systems of types II and III, as well as Timoshenko-type systems with past history. Part of the book is based on the research conducted by the authors and their collaborators in recent years. The book will benefit interested beginners in the field and experts alike.

Modern Aspects of the Theory of Partial Differential Equations

Modern Aspects of the Theory of Partial Differential Equations
Author: Michael Ruzhansky
Publisher: Springer Science & Business Media
Total Pages: 366
Release: 2011-05-04
Genre: Mathematics
ISBN: 303480069X

The book provides a quick overview of a wide range of active research areas in partial differential equations. The book can serve as a useful source of information to mathematicians, scientists and engineers. The volume contains contributions from authors from a large variety of countries on different aspects of partial differential equations, such as evolution equations and estimates for their solutions, control theory, inverse problems, nonlinear equations, elliptic theory on singular domains, numerical approaches.

Qualitative Aspects And Applications Of Nonlinear Evolution Equations - Proceedings Of The Workshop

Qualitative Aspects And Applications Of Nonlinear Evolution Equations - Proceedings Of The Workshop
Author: H Beirao Da Veiga
Publisher: World Scientific
Total Pages: 230
Release: 1994-05-31
Genre:
ISBN: 981455166X

This book provides an introduction for graduate students and advanced undergraduate students to the field of astrophysical fluid dynamics. Although sometimes ignored, fluid dynamical processes play a central role in virtually all areas of astrophysics.No previous knowledge of fluid dynamics is assumed. After establishing the basic equations of fluid dynamics and the physics relevant to an astrophysical application, a variety of topics in the field are addressed. There is also a chapter introducing the reader to numerical methods. Appendices list useful physical constants and astronomical quantities, and provide handy reference material on Cartesian tensors, vector calculus in polar coordinates, self-adjoint eigenvalue problems and JWKB theory./a

Global Existence and Uniqueness of Nonlinear Evolutionary Fluid Equations

Global Existence and Uniqueness of Nonlinear Evolutionary Fluid Equations
Author: Yuming Qin
Publisher: Birkhäuser
Total Pages: 217
Release: 2015-02-11
Genre: Science
ISBN: 3034805942

This book presents recent results on nonlinear evolutionary fluid equations such as the compressible (radiative) magnetohydrodynamics (MHD) equations, compressible viscous micropolar fluid equations, the full non-Newtonian fluid equations and non-autonomous compressible Navier-Stokes equations. These types of partial differential equations arise in many fields of mathematics, but also in other branches of science such as physics and fluid dynamics. This book will be a valuable resource for graduate students and researchers interested in partial differential equations, and will also benefit practitioners in physics and engineering.

Handbook of Differential Equations: Evolutionary Equations

Handbook of Differential Equations: Evolutionary Equations
Author: C.M. Dafermos
Publisher: Elsevier
Total Pages: 579
Release: 2004-08-24
Genre: Mathematics
ISBN: 0080521827

This book contains several introductory texts concerning the main directions in the theory of evolutionary partial differential equations. The main objective is to present clear, rigorous,and in depth surveys on the most important aspects of the present theory. The table of contents includes: W.Arendt: Semigroups and evolution equations: Calculus, regularity and kernel estimatesA.Bressan: The front tracking method for systems of conservation lawsE.DiBenedetto, J.M.Urbano,V.Vespri: Current issues on singular and degenerate evolution equations;L.Hsiao, S.Jiang: Nonlinear hyperbolic-parabolic coupled systemsA.Lunardi: Nonlinear parabolic equations and systemsD.Serre:L1-stability of nonlinear waves in scalar conservation laws B.Perthame:Kinetic formulations of parabolic and hyperbolic PDE's: from theory to numerics