Viscoelasticity and Rheology covers the proceedings of a symposium by the same title, conducted by the Mathematics Research Center held at the University of Wisconsin-Madison on October 16-18, 1984. The contributions to the symposium are divided into four broad categories, namely, experimental results, constitutive theories, mathematical analysis, and computation.This 16-chapter work begins with experimental topics, including the motion of bubbles in viscoelastic fluids, wave propagation in viscoelastic solids, flows through contractions, and cold-drawing of polymers. The next chapters covering constitutive theories explore the molecular theories for polymer solutions and melts based on statistical mechanics, the use and limitations of approximate constitutive theories, a comparison of constitutive laws based on various molecular theories, network theories and some of their advantages in relation to experiments, and models for viscoplasticity. These topics are followed by discussions of the existence, regularity, and development of singularities, change of type, interface problems in viscoelasticity, existence for initial value problems and steady flows, and propagation and development of singularities. The remaining chapters deal with the numerical simulation of flow between eccentric cylinders, flow around spheres and bubbles, the hole pressure problem, and a review of computational problems related to various constitutive laws.This book will prove useful to chemical engineers, researchers, and students.

Viscoelasticity and Rheology (Publication of the Mathematics Research Center, the University of Wisconsin-Madison, No 53)

Science & Math

Renardy, Michael

Lodge, Arthur S.

Mathematics

Academic Pr

Partial differential equations are fundamental to the modeling of natural phenomena. The desire to understand the solutions of these equations has always had a prominent place in the efforts of mathematicians and has inspired such diverse fields as complex function theory, functional analysis, and algebraic topology. This book, meant for a beginning graduate audience, provides a thorough introduction to partial differential equations.

An Introduction to Partial Differential Equations (Texts in Applied Mathematics, 13)

Rogers, Robert C.

Springer

This book is intended for a three or four semester course in "Partial Differential Equations". It is based on a four-semester course taught at Virginia Polytechnic Institute and State University. The goal of this class was to provide the background necessary to initiate work on a PhD thesis in partial differential equations. The book opens with an introduction to the subject matter and its characteristics which contain the Cauchy-Kovalevskaya Theorem and Holmgren's Uniqueness Theorem. Conversation laws and shocks are then covered, followed by maximum principles and function spaces. Linear elliptic equations and nonlinear elliptic equations are also included. The text concludes with energy methods for evolution problems and semigroup methods. In the standard graduate curriculum, the subject of partial differential equations is seldom taught with the same thoroughness as algebra or integration theory. This book is aimed at rectifying the situation, by going further than the competition. There are numerous other textbooks on partial differential equations, but few are directed at a beginning graduate audience as this one is. The level of the book is aimed at beginning graduate students. Prerequisites include a truly advanced calculus course and basic complex variables, but no knowledge is required of Lebesque integration theory or functional analysis. This book provides a thorough introduction to partial differential equations, bringing the students up to the level at which research can begin.

An Introduction to Partial Differential Equations (Texts in Applied Mathematics)

SPRINGER @ NY INC

Mathematical Problems in Viscoelasticity (CHAPMAN AND HALL /CRC MONOGRAPHS AND SURVEYS IN PURE AND APPLIED MATHEMATICS)

Nohel, John A.

Hrusa, William J.

Longman Sc & Tech

The flow behavior of fluids such as molten plastics, biological fluids, and paints is much more varied and complex than that of traditional Newtonian fluids. The role of numerical simulation in the study of such flows has increased tremendously over the past fifteen years, and the phenomena and numerical difficulties in complex flows have led to new and challenging mathematical questions. Studying such flows presents a host of problems, as well as opportunities for mathematical analysis, including questions of asymptotics, qualitative dynamics, and adequacy of numerical methods. Mathematical Analysis of Viscoelastic Flows presents an overview of mathematical problems, methods, and results relating to research on viscoelastic flows.

Mathematical Analysis of Viscoelastic Flows (Classics in Applied Mathematics, Series Number 73)

Society for Industrial and Applied Mathematics

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