Crandall, Michael G.
Overview
Works:  77 works in 279 publications in 1 language and 1,297 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Commentator 
Classifications:  QA3, 515.353 
Publication Timeline
.
Most widely held works by
Michael G Crandall
Nonlinear evolution equations : proceedings of a symposium by University of Wisconsin  Madison Symposium on Nonlinear Evolution Equations(
Book
)
30 editions published between 1977 and 1978 in English and Undetermined and held by 353 WorldCat member libraries worldwide
This volume constitutes the proceedings of the Symposium on Nonlinear Evolution Equations held in Madison, October 1719, 1977. The thirteen papers presented here follow the order of the corresponding lectures. J. Moser's lecture, 'Differential Equations Connected with IsoSpectral Deformations, ' is not represented in this volume. However, the relevant material is forthcoming in a joint article by J. Moser and M. Adler in Comm. Math. Phys. (1978). This symposium was sponsored by the Army Research Office, the National Science Foundation, and the Office of Naval Research. Among those who contributed to the success of the symposium John A. Nohel, our cochairman, deserves special mention. Hearty thanks are also due to the speakers, the chairmen of the sessions, our peerless symposium secretary Mrs. Gladys G. Moran, and the outstanding group of participants who made the symposium such an exceptional event. The cheerful competence of Judith Siesen was indispensable in preparing this volume. (Author)
30 editions published between 1977 and 1978 in English and Undetermined and held by 353 WorldCat member libraries worldwide
This volume constitutes the proceedings of the Symposium on Nonlinear Evolution Equations held in Madison, October 1719, 1977. The thirteen papers presented here follow the order of the corresponding lectures. J. Moser's lecture, 'Differential Equations Connected with IsoSpectral Deformations, ' is not represented in this volume. However, the relevant material is forthcoming in a joint article by J. Moser and M. Adler in Comm. Math. Phys. (1978). This symposium was sponsored by the Army Research Office, the National Science Foundation, and the Office of Naval Research. Among those who contributed to the success of the symposium John A. Nohel, our cochairman, deserves special mention. Hearty thanks are also due to the speakers, the chairmen of the sessions, our peerless symposium secretary Mrs. Gladys G. Moran, and the outstanding group of participants who made the symposium such an exceptional event. The cheerful competence of Judith Siesen was indispensable in preparing this volume. (Author)
Directions in partial differential equations by
Michael G Crandall(
Book
)
20 editions published between 1987 and 2014 in English and Undetermined and held by 258 WorldCat member libraries worldwide
Directions in Partial Differential Equations
20 editions published between 1987 and 2014 in English and Undetermined and held by 258 WorldCat member libraries worldwide
Directions in Partial Differential Equations
Viscosity solutions of partial differential equations by
Michael G Crandall(
Visual
)
5 editions published between 1990 and 2008 in English and held by 13 WorldCat member libraries worldwide
Live recording of a lecture by Michael Crandall at which he presents an expository introduction to the theory of viscosity solutions of parital differential equations
5 editions published between 1990 and 2008 in English and held by 13 WorldCat member libraries worldwide
Live recording of a lecture by Michael Crandall at which he presents an expository introduction to the theory of viscosity solutions of parital differential equations
Regularizing effects for u[t] + A[phi](u) = 0 in L1 by
Michael G Crandall(
Book
)
8 editions published between 1980 and 1981 in English and held by 9 WorldCat member libraries worldwide
8 editions published between 1980 and 1981 in English and held by 9 WorldCat member libraries worldwide
A semilinear elliptic equation in L 1 (IR N) by
P Bénilan(
Book
)
6 editions published in 1975 in English and held by 7 WorldCat member libraries worldwide
6 editions published in 1975 in English and held by 7 WorldCat member libraries worldwide
Regularizing effects of homogeneous evolution equations by
Michael G Crandall(
Book
)
5 editions published in 1980 in English and held by 7 WorldCat member libraries worldwide
It is wellknown that solving the initialvalue problem for the heat equation forward in time takes a 'rough' initial temperature into a temperature which is smooth at later times t> greater than 0. One aspect of this is the validity of certain estimates on tut when u is a solution of the heat equation. In this paper we prove related estimates on nonlinear evolution equations which are governed by homogeneous nonlinearities. The results apply to classes of nonlinear diffusion equations and to conservation laws. The results are interesting from the point of view of identifying a new 'regularization' mechanism and the estimates themselves cast new light on the nature of the solutions of some initialvalue problems with rough initial data
5 editions published in 1980 in English and held by 7 WorldCat member libraries worldwide
It is wellknown that solving the initialvalue problem for the heat equation forward in time takes a 'rough' initial temperature into a temperature which is smooth at later times t> greater than 0. One aspect of this is the validity of certain estimates on tut when u is a solution of the heat equation. In this paper we prove related estimates on nonlinear evolution equations which are governed by homogeneous nonlinearities. The results apply to classes of nonlinear diffusion equations and to conservation laws. The results are interesting from the point of view of identifying a new 'regularization' mechanism and the estimates themselves cast new light on the nature of the solutions of some initialvalue problems with rough initial data
Some relations between nonexpansive and order preserving mappings by
Michael G Crandall(
Book
)
4 editions published in 1979 in English and held by 6 WorldCat member libraries worldwide
It is shown that nonlinear operators which preserve the integral are order preserving if and only if they are nonexpansive in L(1) and that those wich commute with translation by a constant are order preserving if and only if they are nonexpansive in L(infinity). Examples are presented and involving partial differential equations, difference approximations and rearrangements. (Author)
4 editions published in 1979 in English and held by 6 WorldCat member libraries worldwide
It is shown that nonlinear operators which preserve the integral are order preserving if and only if they are nonexpansive in L(1) and that those wich commute with translation by a constant are order preserving if and only if they are nonexpansive in L(infinity). Examples are presented and involving partial differential equations, difference approximations and rearrangements. (Author)
Bifurcation, perturbation of simple eigenvalues and linearized stability by
Michael G Crandall(
Book
)
5 editions published between 1972 and 1973 in English and held by 6 WorldCat member libraries worldwide
The eigenvalue of minimum modulus of the Frechet derivative of a nonlinear operator is estimated along a bifurcating curve of zeroes of the operator. This result is applied to the study of a number of differential equations. Parallel results are developed for a class of nonlinear eigenvalue problems of positive type. (Author)
5 editions published between 1972 and 1973 in English and held by 6 WorldCat member libraries worldwide
The eigenvalue of minimum modulus of the Frechet derivative of a nonlinear operator is estimated along a bifurcating curve of zeroes of the operator. This result is applied to the study of a number of differential equations. Parallel results are developed for a class of nonlinear eigenvalue problems of positive type. (Author)
On the relation of the operator [delta]/[delta]s + [delta]/[delta]t to evolution governed by accretive operators by
Michael G Crandall(
Book
)
5 editions published in 1975 in English and held by 6 WorldCat member libraries worldwide
5 editions published in 1975 in English and held by 6 WorldCat member libraries worldwide
Remarks on Generators of Analytic Semigroups by
Michael G Crandall(
Book
)
5 editions published in 1979 in English and held by 5 WorldCat member libraries worldwide
This paper contains two new characterizations of generators of analytic semigroups of linear operators in a Banach space. These characterizations do not require use of complex numbers. One is used to give a new proof that strongly elliptic second order partial differential operators generate analytic semigroups in L superscript p, 1 <p <infinity, while the sufficient condition in the other characterization is meaningful in the case of nonlinear operators. (Author)
5 editions published in 1979 in English and held by 5 WorldCat member libraries worldwide
This paper contains two new characterizations of generators of analytic semigroups of linear operators in a Banach space. These characterizations do not require use of complex numbers. One is used to give a new proof that strongly elliptic second order partial differential operators generate analytic semigroups in L superscript p, 1 <p <infinity, while the sufficient condition in the other characterization is meaningful in the case of nonlinear operators. (Author)
Viscosity Solutions of HamiltonJacobi Equations by
Michael G Crandall(
Book
)
6 editions published between 1981 and 1983 in English and held by 5 WorldCat member libraries worldwide
Problems involving HamiltonJacobi equations  which we take to be either of the stationary form H(X, u, Du) = 0 or of the evolution form u sub t + H(x, t, u, Du) = 0, where Du is the spatial gradient of u  arise in many contexts. Classical analysis of associated problems under boundary and/or initial conditions by the method of characteristics is limited to local considerations owing to the crossing of characteristics. Global analysis of these problems has been hindered by the lack of an appropriate notion of solution for which one has the desired existence and uniqueness properties. In this work a notion of solution is proposed which allows, for example, solutions to be nowhere differentiable but for which strong uniqueness theorems, stability theorems and general existence theorems, as discussed herein, are all valid
6 editions published between 1981 and 1983 in English and held by 5 WorldCat member libraries worldwide
Problems involving HamiltonJacobi equations  which we take to be either of the stationary form H(X, u, Du) = 0 or of the evolution form u sub t + H(x, t, u, Du) = 0, where Du is the spatial gradient of u  arise in many contexts. Classical analysis of associated problems under boundary and/or initial conditions by the method of characteristics is limited to local considerations owing to the crossing of characteristics. Global analysis of these problems has been hindered by the lack of an appropriate notion of solution for which one has the desired existence and uniqueness properties. In this work a notion of solution is proposed which allows, for example, solutions to be nowhere differentiable but for which strong uniqueness theorems, stability theorems and general existence theorems, as discussed herein, are all valid
A generalized domain for semigroup generators by
Michael G Crandall(
Book
)
5 editions published in 1972 in English and held by 5 WorldCat member libraries worldwide
A generalized domain D(A) is assigned to a certain class of generators A of semigroups of nonlinear transformations S on Banach spaces. D(A) is then characterized in two ways. D(A) is the set of x such that S(t)x is locally Lipschitz continuous in t, or, equivalently, the set of x which can lie in the domain of suitable extensions of A. (Author)
5 editions published in 1972 in English and held by 5 WorldCat member libraries worldwide
A generalized domain D(A) is assigned to a certain class of generators A of semigroups of nonlinear transformations S on Banach spaces. D(A) is then characterized in two ways. D(A) is the set of x such that S(t)x is locally Lipschitz continuous in t, or, equivalently, the set of x which can lie in the domain of suitable extensions of A. (Author)
Viscosity solutions and applications : lectures given at the 2nd session of the Centro internazionale matematico estivo (C.I.M.E.)
held in Montecatini Terme, Italy, June 1220, 1995 by
M Bardi(
Book
)
5 editions published in 1997 in English and held by 5 WorldCat member libraries worldwide
The volume comprises five extended surveys on the recent theory of viscosity solutions of fully nonlinear partial differential equations, and some of its most relevant applications to optimal control theory for deterministic and stochastic systems, front propagation, geometric motions and mathematical finance. The volume forms a stateoftheart reference on the subject of viscosity solutions, and the authors are among the most prominent specialists. Potential readers are researchers in nonlinear PDE's, systems theory, stochastic processes
5 editions published in 1997 in English and held by 5 WorldCat member libraries worldwide
The volume comprises five extended surveys on the recent theory of viscosity solutions of fully nonlinear partial differential equations, and some of its most relevant applications to optimal control theory for deterministic and stochastic systems, front propagation, geometric motions and mathematical finance. The volume forms a stateoftheart reference on the subject of viscosity solutions, and the authors are among the most prominent specialists. Potential readers are researchers in nonlinear PDE's, systems theory, stochastic processes
Monotone Difference Approximations for Scalar Conservation Laws by
Michael G Crandall(
Book
)
5 editions published in 1979 in English and held by 5 WorldCat member libraries worldwide
A complete selfcontained treatment of the stability and convergence properties of conservation form, monotone difference approximations to scalar conservation laws in several space variables is developed. In particular, the authors prove that general monotone difference schemes always converge and that they converge to the physical weak solution satisfying the entropy condition. Rigorous convergence results follow for dimensional splitting algorithms when each step is approximated by a monotone difference scheme. The results are general enough to include, for instance, Godunov's scheme, the upwind scheme (Differenced through stagnation points), and the LaxFriedrichs scheme together with appropriate multidimensional generalizations. (Author)
5 editions published in 1979 in English and held by 5 WorldCat member libraries worldwide
A complete selfcontained treatment of the stability and convergence properties of conservation form, monotone difference approximations to scalar conservation laws in several space variables is developed. In particular, the authors prove that general monotone difference schemes always converge and that they converge to the physical weak solution satisfying the entropy condition. Rigorous convergence results follow for dimensional splitting algorithms when each step is approximated by a monotone difference scheme. The results are general enough to include, for instance, Godunov's scheme, the upwind scheme (Differenced through stagnation points), and the LaxFriedrichs scheme together with appropriate multidimensional generalizations. (Author)
An approximation of integrable functions by step functions with an application by
Michael G Crandall(
Book
)
5 editions published between 1978 and 1979 in English and held by 5 WorldCat member libraries worldwide
A method of approximating functions which are integrable on (0, infinity) by piecewise constant functions is presented and studied in this paper. The method used and the properties established for it allow one to reduce the study of the convergence of a difference method of theoretical interest for nonlinear timedependent problems with forcing terms to the simpler study of related problems without forcing terms
5 editions published between 1978 and 1979 in English and held by 5 WorldCat member libraries worldwide
A method of approximating functions which are integrable on (0, infinity) by piecewise constant functions is presented and studied in this paper. The method used and the properties established for it allow one to reduce the study of the convergence of a difference method of theoretical interest for nonlinear timedependent problems with forcing terms to the simpler study of related problems without forcing terms
The Semigroup Approach to First Order Quasilinear Equations in Several Space Variables by
Michael G Crandall(
Book
)
4 editions published in 1972 in English and held by 4 WorldCat member libraries worldwide
The Cauchy problem for (u sub t) + Summation, i = 1 to n, of (phi sub i) (u sub (x sub i)) = 0 is treated via the theory of semigroups of nonlinear transformations. (Author)
4 editions published in 1972 in English and held by 4 WorldCat member libraries worldwide
The Cauchy problem for (u sub t) + Summation, i = 1 to n, of (phi sub i) (u sub (x sub i)) = 0 is treated via the theory of semigroups of nonlinear transformations. (Author)
A Generalization of Peano's Theorem and Flow Invariance by
Michael G Crandall(
Book
)
4 editions published in 1972 in English and held by 4 WorldCat member libraries worldwide
Let F contained in (R sub n) be closed and A:F maps to (R sub n) be continuous. Assuming that the distance from y+hAy to F is o(h) as h tends to 0 +, it is shown that for each x contained in F the Cauchy problem u prime = Au, u(0) = x, has a solution u: (0, T sub x) maps to F on some interval (0, T sub x), (T sub x> 0. (Author)
4 editions published in 1972 in English and held by 4 WorldCat member libraries worldwide
Let F contained in (R sub n) be closed and A:F maps to (R sub n) be continuous. Assuming that the distance from y+hAy to F is o(h) as h tends to 0 +, it is shown that for each x contained in F the Cauchy problem u prime = Au, u(0) = x, has a solution u: (0, T sub x) maps to F on some interval (0, T sub x), (T sub x> 0. (Author)
Calculus of Variations and Nonlinear Partial Differential Equations With a historical overview by Elvira Mascolo by
Luigi Ambrosio(
Book
)
7 editions published in 2008 in English and Undetermined and held by 2 WorldCat member libraries worldwide
This volume provides the texts of lectures given by L. Ambrosio, L. Caffarelli, M. Crandall, L.C. Evans, N. Fusco at the Summer course held in Cetraro (Italy) in 2005. These are introductory reports on current research by world leaders in the fields of calculus of variations and partial differential equations. The topics discussed are transport equations for nonsmooth vector fields, homogenization, viscosity methods for the infinite Laplacian, weak KAM theory and geometrical aspects of symmetrization. A historical overview of all CIME courses on the calculus of variations and partial differential equations is contributed by Elvira Mascolo
7 editions published in 2008 in English and Undetermined and held by 2 WorldCat member libraries worldwide
This volume provides the texts of lectures given by L. Ambrosio, L. Caffarelli, M. Crandall, L.C. Evans, N. Fusco at the Summer course held in Cetraro (Italy) in 2005. These are introductory reports on current research by world leaders in the fields of calculus of variations and partial differential equations. The topics discussed are transport equations for nonsmooth vector fields, homogenization, viscosity methods for the infinite Laplacian, weak KAM theory and geometrical aspects of symmetrization. A historical overview of all CIME courses on the calculus of variations and partial differential equations is contributed by Elvira Mascolo
Nonlinear Evolution Equations by
Michael G Crandall(
)
2 editions published in 2014 in English and held by 0 WorldCat member libraries worldwide
2 editions published in 2014 in English and held by 0 WorldCat member libraries worldwide
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Related Identities
 University of WisconsinMadison Mathematics Research Center Publisher Editor
 Rabinowitz, Paul H. Editor
 Brézis, H. (Haim) Author Editor
 Turner, Robert E. L. Editor
 Kappel, F. Editor
 Evans, Lawrence C.
 Ambrosio, Luigi Commentator Author
 Marcellini, Paolo Editor
 Dacorogna, Bernard Editor
 Caffarelli, Luis Commentator
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Associated Subjects
Analytic mappings Approximation theory Banach spaces Bifurcation theory Canada Cauchy problem Convergence Difference equations Differential equations Differential equations, Elliptic Differential equations, Nonlinear Differential equations, Parabolic Differential equations, Partial Differential invariants Differential operators Distribution (Probability theory) Eigenvalues Evolution equations Evolution equations, Nonlinear Existence theorems Functions HamiltonJacobi equations Inequalities (Mathematics) Initial value problems Mathematical optimization Mathematics Nonlinear operators Peano, Giuseppe, Quasilinearization Scientists Semigroups Transformation groups United States Viscosity Viscosity solutions
Alternative Names
Crandall, M. G.
Crandall, M. G. (Michael G.)
Michael Crandall
Michael Crandall USamerikanischer Mathematiker
Michael G. Crandall Amerikaans wiskundige
Michael G. Crandall amerikansk matematikar
Michael G. Crandall amerikansk matematiker
Michael G. Crandall mathématicien américain
Майкл Крандалл американский математик
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