Renardy, Michael
Overview
Works:  35 works in 111 publications in 2 languages and 2,039 library holdings 

Genres:  Conference proceedings 
Roles:  Author, Editor, Contributor 
Classifications:  QA374, 515.353 
Publication Timeline
.
Most widely held works by
Michael Renardy
An introduction to partial differential equations by
Michael Renardy(
Book
)
43 editions published between 1992 and 2011 in English and Undetermined and held by 872 WorldCat member libraries worldwide
"Partial differential equations (PDEs) are fundamental to the modeling of natural phenomena, arising in every field of science. Consequently, the desire to understand the solutions of these equations has always had a prominent place in the efforts of mathematicians; it has inspired such diverse fields as complex function theory, functional analysis, and algebraic topology. Like algebra, topology, and rational mechanics, PDEs are a core area of mathematics." "This book aims to provide the background necessary to initiate work on a Ph. D. thesis in PDEs for beginning graduate students. Prerequisites include a truly advanced calculus course and basic complex variables. Lebesgue integration is needed only in Chapter 10, and the necessary tools from functional analysis are developed within the course. The book can be used to teach a variety of different courses."Jacket
43 editions published between 1992 and 2011 in English and Undetermined and held by 872 WorldCat member libraries worldwide
"Partial differential equations (PDEs) are fundamental to the modeling of natural phenomena, arising in every field of science. Consequently, the desire to understand the solutions of these equations has always had a prominent place in the efforts of mathematicians; it has inspired such diverse fields as complex function theory, functional analysis, and algebraic topology. Like algebra, topology, and rational mechanics, PDEs are a core area of mathematics." "This book aims to provide the background necessary to initiate work on a Ph. D. thesis in PDEs for beginning graduate students. Prerequisites include a truly advanced calculus course and basic complex variables. Lebesgue integration is needed only in Chapter 10, and the necessary tools from functional analysis are developed within the course. The book can be used to teach a variety of different courses."Jacket
Mathematical problems in viscoelasticity by
Michael Renardy(
Book
)
10 editions published in 1987 in English and held by 220 WorldCat member libraries worldwide
10 editions published in 1987 in English and held by 220 WorldCat member libraries worldwide
Viscoelasticity and rheology by
Arthur S Lodge(
Book
)
9 editions published between 1985 and 2014 in English and held by 214 WorldCat member libraries worldwide
9 editions published between 1985 and 2014 in English and held by 214 WorldCat member libraries worldwide
Mathematical analysis of viscoelastic flows by
Michael Renardy(
Book
)
12 editions published in 2000 in English and held by 209 WorldCat member libraries worldwide
This monograph is based on a series of lectures presented at the 1999 NSFCBMS Regional Research Conference on Mathematical Analysis of Viscoelastic Flows. It begins with an introduction to phenomena observed in viscoelastic flows, the formulation of mathematical equations to model such flows, and the behavior of various models in simple flows. It also discusses the asymptotics of the high Weissenberg limit, the analysis of flow instabilities, the equations of viscoelastic flows, jets and filaments and their breakup, as well as several other topics
12 editions published in 2000 in English and held by 209 WorldCat member libraries worldwide
This monograph is based on a series of lectures presented at the 1999 NSFCBMS Regional Research Conference on Mathematical Analysis of Viscoelastic Flows. It begins with an introduction to phenomena observed in viscoelastic flows, the formulation of mathematical equations to model such flows, and the behavior of various models in simple flows. It also discusses the asymptotics of the high Weissenberg limit, the analysis of flow instabilities, the equations of viscoelastic flows, jets and filaments and their breakup, as well as several other topics
Quasiperiodische Verzweigungslösungen rotationssymmetrischer Probleme by
Michael Renardy(
Book
)
3 editions published in 1980 in German and held by 23 WorldCat member libraries worldwide
3 editions published in 1980 in German and held by 23 WorldCat member libraries worldwide
Existence of slow steady flows of viscoelastic fluids with differential constitutive equations by
Michael Renardy(
Book
)
2 editions published in 1984 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1984 in English and held by 2 WorldCat member libraries worldwide
Special issue on rheological fluid dynamics(
Book
)
1 edition published in 1993 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1993 in English and held by 2 WorldCat member libraries worldwide
LaxWendroff Methods for Hyperbolic History Value Problems by
Mathematics Research Center (United States. Army)(
Book
)
2 editions published in 1982 in English and held by 2 WorldCat member libraries worldwide
The motion of viscoelastic materials can be modelled by partial integrodifferential equations. For several model problems, recent investigations have been concerned with the question whether or not these equations allow the development of shocks. This paper is concerned with LaxWendroff methods for a class of hyperbolic history value problems. These problems have the feature that globally (in time) smooth solutions exist if the data are sufficiently small and that solutions develop singularities for large data. The authors prove (second order) convergence of the LaxWendroff method for smooth solutions and investigate numerically the dependence on the initial data. They demonstrate the occurrence of shock type singularities and compare the results to the quasilinear wave equation (without Volterra term)
2 editions published in 1982 in English and held by 2 WorldCat member libraries worldwide
The motion of viscoelastic materials can be modelled by partial integrodifferential equations. For several model problems, recent investigations have been concerned with the question whether or not these equations allow the development of shocks. This paper is concerned with LaxWendroff methods for a class of hyperbolic history value problems. These problems have the feature that globally (in time) smooth solutions exist if the data are sufficiently small and that solutions develop singularities for large data. The authors prove (second order) convergence of the LaxWendroff method for smooth solutions and investigate numerically the dependence on the initial data. They demonstrate the occurrence of shock type singularities and compare the results to the quasilinear wave equation (without Volterra term)
Singularly Perturbed Hyperbolic Evolution Problems with Infinite Delay and an Application to Polymer Rheology by
Mathematics Research Center (United States. Army)(
Book
)
2 editions published in 1982 in English and held by 2 WorldCat member libraries worldwide
We prove an existence theorem locally in time for quasilinear hyperbolic equations, in which the coefficients are allowed to depend on the history of the dependent variable. Singular perturbations, which change the type of the equation to parabolic, are included, and continuous dependence of the solutions on the perturbation parameter is shown. It is demonstrated that, for a substantial number of constitutive models suggested in the literature, the stretching of filaments of polymeric liquids is described by equations of the kind under study here. (Author)
2 editions published in 1982 in English and held by 2 WorldCat member libraries worldwide
We prove an existence theorem locally in time for quasilinear hyperbolic equations, in which the coefficients are allowed to depend on the history of the dependent variable. Singular perturbations, which change the type of the equation to parabolic, are included, and continuous dependence of the solutions on the perturbation parameter is shown. It is demonstrated that, for a substantial number of constitutive models suggested in the literature, the stretching of filaments of polymeric liquids is described by equations of the kind under study here. (Author)
Perturbation of a Multiple Eigenvalue in the Benard Problem for Two Fluid Layers by
Yuriko Renardy(
Book
)
2 editions published in 1984 in English and held by 2 WorldCat member libraries worldwide
In a recent paper, Renardy and Joseph study the Bernard problem for two layers of different fluids lying on top of each other and bounded by walls. Their study shows that, in contrast to the Benard problem for one fluid, the onset of instability can be oscillatory. The number of parameters involved in the problem is large, and there is yet no comprehensive picture of when the instability is oscillatory and when it is not. The study of limiting cases, accessible by perturbation methods, may be helpful in this respect. In this document, an analysis is given for the case when the properties of the two fluids are nearly equal and the fluids are allowed to slip at the boundaries. (Author)
2 editions published in 1984 in English and held by 2 WorldCat member libraries worldwide
In a recent paper, Renardy and Joseph study the Bernard problem for two layers of different fluids lying on top of each other and bounded by walls. Their study shows that, in contrast to the Benard problem for one fluid, the onset of instability can be oscillatory. The number of parameters involved in the problem is large, and there is yet no comprehensive picture of when the instability is oscillatory and when it is not. The study of limiting cases, accessible by perturbation methods, may be helpful in this respect. In this document, an analysis is given for the case when the properties of the two fluids are nearly equal and the fluids are allowed to slip at the boundaries. (Author)
A Center Manifold theorem for hyperbolic PDEs by
Michael Renardy(
Book
)
1 edition published in 1991 in English and held by 1 WorldCat member library worldwide
1 edition published in 1991 in English and held by 1 WorldCat member library worldwide
Local existence of solutions of the Dirichlet initialboundary value problem of incompressible hypoelastic materials by
Michael Renardy(
Book
)
1 edition published in 1988 in English and held by 1 WorldCat member library worldwide
1 edition published in 1988 in English and held by 1 WorldCat member library worldwide
Existence of slow steady flows of viscoelastic fluids with differential constitutive equations by
Mathematics Research Center (United States. Army)(
Book
)
1 edition published in 1984 in English and held by 1 WorldCat member library worldwide
1 edition published in 1984 in English and held by 1 WorldCat member library worldwide
Inflow Boundary Conditions for Steady Flows of Viscoelastic Fluids with Differential Constitutive Laws by
Michael Renardy(
Book
)
1 edition published in 1986 in Undetermined and held by 1 WorldCat member library worldwide
1 edition published in 1986 in Undetermined and held by 1 WorldCat member library worldwide
On the domain space for constitutive laws in linear viscoelasticity by
Mathematics Research Center (United States. Army)(
Book
)
1 edition published in 1982 in English and held by 1 WorldCat member library worldwide
1 edition published in 1982 in English and held by 1 WorldCat member library worldwide
A first graduate course in partial differential equations by
Michael Renardy(
Book
)
1 edition published in 1993 in English and held by 1 WorldCat member library worldwide
1 edition published in 1993 in English and held by 1 WorldCat member library worldwide
Rheological fluid dynamics(
Book
)
1 edition published in 1993 in English and held by 1 WorldCat member library worldwide
1 edition published in 1993 in English and held by 1 WorldCat member library worldwide
Inflow Boundary Conditions for Steady Flows of Viscoelastic Fluids with Differential Constitutive Laws(
Book
)
1 edition published in 1986 in English and held by 1 WorldCat member library worldwide
Steady flows of viscoelastic fluids can not be uniquely determined by imposing boundary conditions only for the velocities as in the Newtonian case. The reason for this is that the fluids have memory, and therefore the flow inside the domain is affected by what happened before the fluid entered the domain. This leads to the need for extra boundary conditions at an inflow boundary. The nature of these inflow boundary conditions has not been analyzed previously, and it is certainly dependent on the constitutive law. In this paper, we look at the special case of differential constitutive relations with a single relaxation mode. We consider steady transverse flows across a strip which are small perturbations of a flow with constant velocity. It turns out that in this case two extra inflow boundary conditions are required in two dimensions, and four in three dimensions. This is what would be expected from an analysis of characteristics, but it contradicts the belief of many rheologists that it is possible to prescribe the extra stress at an inflow boundary. The problem studied here is of potential relevance for numerical simulations of steady flows. Many of the flows currently simulated are on infinite domains. Numerically, these domains are truncated, and on the inflow boundary of the truncated domain people usually prescribe the extra stress. According to the analysis in this paper, this is an overdetermined problem, and therefore errors must be expected from this procedure unless the artificial boundaries are chosen far enough out. Keywords: Upper Convected Maxwell Model
1 edition published in 1986 in English and held by 1 WorldCat member library worldwide
Steady flows of viscoelastic fluids can not be uniquely determined by imposing boundary conditions only for the velocities as in the Newtonian case. The reason for this is that the fluids have memory, and therefore the flow inside the domain is affected by what happened before the fluid entered the domain. This leads to the need for extra boundary conditions at an inflow boundary. The nature of these inflow boundary conditions has not been analyzed previously, and it is certainly dependent on the constitutive law. In this paper, we look at the special case of differential constitutive relations with a single relaxation mode. We consider steady transverse flows across a strip which are small perturbations of a flow with constant velocity. It turns out that in this case two extra inflow boundary conditions are required in two dimensions, and four in three dimensions. This is what would be expected from an analysis of characteristics, but it contradicts the belief of many rheologists that it is possible to prescribe the extra stress at an inflow boundary. The problem studied here is of potential relevance for numerical simulations of steady flows. Many of the flows currently simulated are on infinite domains. Numerically, these domains are truncated, and on the inflow boundary of the truncated domain people usually prescribe the extra stress. According to the analysis in this paper, this is an overdetermined problem, and therefore errors must be expected from this procedure unless the artificial boundaries are chosen far enough out. Keywords: Upper Convected Maxwell Model
The Numerical Solution of a Class of Quasilinear Parabolic Volterra Equations Arising in Polymer Rheology(
Book
)
1 edition published in 1983 in English and held by 1 WorldCat member library worldwide
1 edition published in 1983 in English and held by 1 WorldCat member library worldwide
Local existence and uniqueness theorem for a K  BKZ  fluid by
Mathematics Research Center (United States. Army)(
Book
)
1 edition published in 1983 in English and held by 1 WorldCat member library worldwide
1 edition published in 1983 in English and held by 1 WorldCat member library worldwide
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Related Identities
 Rogers, Robert C.
 Nohel, John A. Contributor Editor
 Lodge, Arthur S. Author Editor
 University of WisconsinMadison Mathematics Research Center Editor
 Hrusa, W. (William)
 WISCONSIN UNIVMADISON MATHEMATICS RESEARCH CENTER
 Society for Industrial and Applied Mathematics
 MyiLibrary (Service en ligne)
 Mathematics Research Center (United States. Army)
 Rogers, R. C.