Nohel, John A.
Overview
Works:  72 works in 295 publications in 3 languages and 3,445 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Editor, Author, Contributor 
Classifications:  QA372, 517.382 
Publication Timeline
.
Most widely held works by
John A Nohel
The qualitative theory of ordinary differential equations; an introduction by
Fred Brauer(
Book
)
29 editions published between 1969 and 2012 in English and held by 649 WorldCat member libraries worldwide
Superb, selfcontained graduatelevel text covers standard theorems concerning linear systems, existence and uniqueness of solutions, and dependence on parameters. Major focus on stability theory and its applications to oscillation phenomena, selfexcited oscillations and regulator problem of Lurie
29 editions published between 1969 and 2012 in English and held by 649 WorldCat member libraries worldwide
Superb, selfcontained graduatelevel text covers standard theorems concerning linear systems, existence and uniqueness of solutions, and dependence on parameters. Major focus on stability theory and its applications to oscillation phenomena, selfexcited oscillations and regulator problem of Lurie
Ordinary differential equations; a first course by
Fred Brauer(
Book
)
29 editions published between 1967 and 1973 in 3 languages and held by 545 WorldCat member libraries worldwide
29 editions published between 1967 and 1973 in 3 languages and held by 545 WorldCat member libraries worldwide
Linear mathematics; an introduction to linear algebra and linear differential equations by
Fred Brauer(
Book
)
11 editions published in 1970 in English and Undetermined and held by 387 WorldCat member libraries worldwide
11 editions published in 1970 in English and Undetermined and held by 387 WorldCat member libraries worldwide
Problems and solutions in ordinary differential equations by
Fred Brauer(
Book
)
13 editions published between 1968 and 1970 in English and Italian and held by 236 WorldCat member libraries worldwide
13 editions published between 1968 and 1970 in English and Italian and held by 236 WorldCat member libraries worldwide
Elementary differential equations: principles, problems, and solutions by
Fred Brauer(
Book
)
8 editions published in 1968 in English and held by 233 WorldCat member libraries worldwide
8 editions published in 1968 in English and held by 233 WorldCat member libraries worldwide
Mathematical problems in viscoelasticity by
Michael Renardy(
Book
)
11 editions published in 1987 in English and held by 221 WorldCat member libraries worldwide
11 editions published in 1987 in English and held by 221 WorldCat member libraries worldwide
Viscoelasticity and rheology by
Arthur S Lodge(
Book
)
10 editions published between 1985 and 2014 in English and held by 213 WorldCat member libraries worldwide
10 editions published between 1985 and 2014 in English and held by 213 WorldCat member libraries worldwide
Advances in differential and integral equations; a collection of papers by Conference on Qualitative Theory of Nonlinear Differential and Integral Equations(
Book
)
4 editions published in 1969 in English and held by 204 WorldCat member libraries worldwide
4 editions published in 1969 in English and held by 204 WorldCat member libraries worldwide
Introduction to differential equations with applications by
Fred Brauer(
Book
)
7 editions published in 1986 in English and held by 151 WorldCat member libraries worldwide
7 editions published in 1986 in English and held by 151 WorldCat member libraries worldwide
Selected papers of Norman Levinson by
Norman Levinson(
Book
)
8 editions published in 1998 in English and held by 105 WorldCat member libraries worldwide
8 editions published in 1998 in English and held by 105 WorldCat member libraries worldwide
Ordinary differential equations : elementary and intermediate topics with applications by
Fred Brauer(
Book
)
8 editions published in 1966 in English and held by 80 WorldCat member libraries worldwide
8 editions published in 1966 in English and held by 80 WorldCat member libraries worldwide
Advances in differential and integral equations : a collection of papers presented at the Conference on Qualitative Theory
of Nonlinear Differential and Integral Equations, held at the University of Wisconsin, August 1223, 1968 by
John A Nohel(
Book
)
17 editions published in 1969 in English and held by 38 WorldCat member libraries worldwide
17 editions published in 1969 in English and held by 38 WorldCat member libraries worldwide
Qualitative theory of ordinary differential equations by
Fred Brauer(
Book
)
4 editions published between 1969 and 1989 in English and held by 17 WorldCat member libraries worldwide
4 editions published between 1969 and 1989 in English and held by 17 WorldCat member libraries worldwide
Asymptotic properties of solutions of nonlinear abstract volterra equations by
Philippe Clément(
Book
)
6 editions published between 1980 and 1981 in English and held by 8 WorldCat member libraries worldwide
The purpose of this paper is to develop a general theory which gives sufficient conditions in terms of the kernel b, the operator A, and the forcing term f for the solution u of (V) to be bounded on t greater than or = 0 but less than infinity and which further assures that the solution u tends to a limit u sub infinity as t approaches infinity; under certain conditions u sub infinity = 0, under others u sub infinity is the unique solution of an appropriate 'limit equation' associated with (V). As one special case of this theory we give a complete analysis of the boundedness and asymptotic properties of the solution of the above heat flow problem, under physically reasonable assumptions concerning the relaxation functions, the nonlinear operator, the initial temperature distribution, and the external heat supply
6 editions published between 1980 and 1981 in English and held by 8 WorldCat member libraries worldwide
The purpose of this paper is to develop a general theory which gives sufficient conditions in terms of the kernel b, the operator A, and the forcing term f for the solution u of (V) to be bounded on t greater than or = 0 but less than infinity and which further assures that the solution u tends to a limit u sub infinity as t approaches infinity; under certain conditions u sub infinity = 0, under others u sub infinity is the unique solution of an appropriate 'limit equation' associated with (V). As one special case of this theory we give a complete analysis of the boundedness and asymptotic properties of the solution of the above heat flow problem, under physically reasonable assumptions concerning the relaxation functions, the nonlinear operator, the initial temperature distribution, and the external heat supply
Nonlinear volterra equations for heat flow in materials with memory by
John A Nohel(
Book
)
5 editions published between 1980 and 1981 in English and held by 7 WorldCat member libraries worldwide
Consider the nonlinear Volterra equation u(t) + (b*Au) not an element of f(t). This paper discusses existing and recent results for the following problems concerning this equation the global existence and uniqueness of solutions and their continuous dependence on the data; the boundedness and asymptotic behavior as t approaches infinity in th special cases when X = H is a real Hilbert space and A is either a maximal monotone operator on H or A is a subdifferential of a proper, convex, lower semicontinuous function; and the existence, boundedness, and asymptotic behavior of positive solutions in the general settting. The theory is used to study one possible model problem for heat flow in a material with 'memory' which can be transformed to the equivalent from of the equation under physically reasonable assumptions; the latter provide a motivation for the natural setting of much of the theory developed here
5 editions published between 1980 and 1981 in English and held by 7 WorldCat member libraries worldwide
Consider the nonlinear Volterra equation u(t) + (b*Au) not an element of f(t). This paper discusses existing and recent results for the following problems concerning this equation the global existence and uniqueness of solutions and their continuous dependence on the data; the boundedness and asymptotic behavior as t approaches infinity in th special cases when X = H is a real Hilbert space and A is either a maximal monotone operator on H or A is a subdifferential of a proper, convex, lower semicontinuous function; and the existence, boundedness, and asymptotic behavior of positive solutions in the general settting. The theory is used to study one possible model problem for heat flow in a material with 'memory' which can be transformed to the equivalent from of the equation under physically reasonable assumptions; the latter provide a motivation for the natural setting of much of the theory developed here
A nonlinear hyperbolic volterra equation in viscoelasticity by
C. M Dafermos(
Book
)
4 editions published in 1980 in English and held by 6 WorldCat member libraries worldwide
A general model for the nonlinear motion of a one dimensional, finite, homogeneous, viscoelastic body is developed and analysed by an energy method. It is shown that under physically reasonable conditions the nonlinear boundary, initial value problem has a unique, smooth solution (global in time), provided the given data are sufficiently 'small' and smooth, moreover, the solution and its derivatives of first and second order decay to zero as t yields infinity. Various modifications and generalizations, including two and three dimensional problems, are also discussed
4 editions published in 1980 in English and held by 6 WorldCat member libraries worldwide
A general model for the nonlinear motion of a one dimensional, finite, homogeneous, viscoelastic body is developed and analysed by an energy method. It is shown that under physically reasonable conditions the nonlinear boundary, initial value problem has a unique, smooth solution (global in time), provided the given data are sufficiently 'small' and smooth, moreover, the solution and its derivatives of first and second order decay to zero as t yields infinity. Various modifications and generalizations, including two and three dimensional problems, are also discussed
Selected papers of Norman Levinson by
Norman Levinson(
Book
)
4 editions published in 1998 in English and held by 5 WorldCat member libraries worldwide
4 editions published in 1998 in English and held by 5 WorldCat member libraries worldwide
Asymptotic behaviour of positive solutions of nonlinear volterra equations for heat flow by
Philippe Clément(
Book
)
5 editions published in 1980 in English and held by 5 WorldCat member libraries worldwide
This report considers nonlinear heat flow in a homogeneous bar of unit length of a material with memory with the ends of the rod maintained at zero temperature and with the history of temperature prescribed for time t less than or = 0. For such materials the internal energy and heat flux are functionals (rather than functions) of the temperature and of the gradient of temperature respectively. Application of the law of balance of heat leads to a nonlinear Volterra integrodifferential equation, together with appropriate boundary and initial conditions, which model the physical problem. This initial boundary value problem, which cannot be solved explicitly and which is difficult to analyse, can be transformed by standard methods to the general equation (V) given in the Abstract. The resulting kernel b can be expressed in terms of the internal energy and heat flux relaxation functions. These are presumed to be known for the physical problem. The operator A in (V) is a nonlinear differential operator together with boundary conditions, and the forcing term f in (V) depends on the given initial temperature distribution, the given external heat supply, and the given history of temperature
5 editions published in 1980 in English and held by 5 WorldCat member libraries worldwide
This report considers nonlinear heat flow in a homogeneous bar of unit length of a material with memory with the ends of the rod maintained at zero temperature and with the history of temperature prescribed for time t less than or = 0. For such materials the internal energy and heat flux are functionals (rather than functions) of the temperature and of the gradient of temperature respectively. Application of the law of balance of heat leads to a nonlinear Volterra integrodifferential equation, together with appropriate boundary and initial conditions, which model the physical problem. This initial boundary value problem, which cannot be solved explicitly and which is difficult to analyse, can be transformed by standard methods to the general equation (V) given in the Abstract. The resulting kernel b can be expressed in terms of the internal energy and heat flux relaxation functions. These are presumed to be known for the physical problem. The operator A in (V) is a nonlinear differential operator together with boundary conditions, and the forcing term f in (V) depends on the given initial temperature distribution, the given external heat supply, and the given history of temperature
A nonlinear integral equation occurring in a singular free boundary problem by
Klaus Höllig(
Book
)
5 editions published between 1983 and 1984 in English and held by 4 WorldCat member libraries worldwide
One motivation for the study of the Cauchy problem is its similarity with the wellknown one phase Stefan problem (in one space dimension). The principal motivation for the study of this problem is that it serves as a prototype of nonlinear parabolic problems which arise as monotone convexifications of nonlinear diffusion equations with nonmonotone constitutive functions phi
5 editions published between 1983 and 1984 in English and held by 4 WorldCat member libraries worldwide
One motivation for the study of the Cauchy problem is its similarity with the wellknown one phase Stefan problem (in one space dimension). The principal motivation for the study of this problem is that it serves as a prototype of nonlinear parabolic problems which arise as monotone convexifications of nonlinear diffusion equations with nonmonotone constitutive functions phi
Analysis and continuum mechanics : a collection of papers dedicated to J. Serrin on his sixtieth birthday by
S. S Antman(
)
1 edition published in 1989 in English and held by 0 WorldCat member libraries worldwide
The 39 papers in this collection are devoted mostly to the exact mathematical analysis of problems in continuum mechanics, but also to problems of a purely mathematical nature mainly connected to partial differential equations from continuum physics. All the papers are dedicated to J. Serrin and were originally published in the "Archive of Rational Mechanics and Analysis."
1 edition published in 1989 in English and held by 0 WorldCat member libraries worldwide
The 39 papers in this collection are devoted mostly to the exact mathematical analysis of problems in continuum mechanics, but also to problems of a purely mathematical nature mainly connected to partial differential equations from continuum physics. All the papers are dedicated to J. Serrin and were originally published in the "Archive of Rational Mechanics and Analysis."
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Related Identities
 Brauer, Fred Author
 Renardy, Michael Contributor Author Editor
 Schneider, Hans 1927 January 24
 Lodge, Arthur S. Author Editor
 University of WisconsinMadison Mathematics Research Center Editor
 Hrusa, W. (William) Author
 Society for Industrial and Applied Mathematics
 University of WisconsinMadison
 Levinson, Norman 19121975 Author
 Sattinger, David H. Editor
Associated Subjects
Algebras, Linear Asymptotes Continuum mechanics Differential algebra Differential equations Differential equations, Linear Differential equations, Nonlinear Differential equations, NonlinearAsymptotic theory HeatMathematical models HeatTransmission Integral equations Mathematical analysis Mathematical physics Mathematicians Mathematics Mechanics Physics Rheology Serrin, J.(James), Stability United States Viscoelasticity ViscoelasticityMathematical models Volterra equations