Evans, L. C.
Overview
Works:  26 works in 43 publications in 1 language and 44 library holdings 

Genres:  Conference proceedings Sermons 
Roles:  Author, Editor 
Classifications:  QA372, 515.353 
Publication Timeline
.
Most widely held works by
L. C Evans
Phase transitions and generalized motion by mean curvature
by
L. C Evans(
Book
)
4 editions published between 1990 and 1991 in English and held by 4 WorldCat member libraries worldwide
Abstract: "We study the limiting behavior of solutions to appropriately rescaled versions of the AllenCahn equation, a model for phase transition in polycrystalline material. We rigourously establish the existence in the limit of a phaseantiphase interface evolving according to mean curvature motion. This assertion is valid for all positive time, the motion interpreted in the generalized sense of EvansSpruck and ChenGigaGoto after the onset of geometric singularities."
4 editions published between 1990 and 1991 in English and held by 4 WorldCat member libraries worldwide
Abstract: "We study the limiting behavior of solutions to appropriately rescaled versions of the AllenCahn equation, a model for phase transition in polycrystalline material. We rigourously establish the existence in the limit of a phaseantiphase interface evolving according to mean curvature motion. This assertion is valid for all positive time, the motion interpreted in the generalized sense of EvansSpruck and ChenGigaGoto after the onset of geometric singularities."
On the relation of the operator [delta]/[delta]s + [delta]/[delta]t to evolution governed by accretive operators
by
Michael G Crandall(
Book
)
3 editions published in 1975 in English and held by 4 WorldCat member libraries worldwide
3 editions published in 1975 in English and held by 4 WorldCat member libraries worldwide
Fast/slow diffusion and growing sandpiles
by
Gunnar Aronsson(
Book
)
4 editions published between 1965 and 1996 in English and held by 4 WorldCat member libraries worldwide
4 editions published between 1965 and 1996 in English and held by 4 WorldCat member libraries worldwide
MiniWorkshop : Partial differential equations ; August 5th  August 11th, 2001
(
Book
)
1 edition published in 2001 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 2001 in English and held by 3 WorldCat member libraries worldwide
An asymptotic model for compression molding
by G Aronsson(
Book
)
3 editions published in 2001 in English and held by 3 WorldCat member libraries worldwide
3 editions published in 2001 in English and held by 3 WorldCat member libraries worldwide
Viscosity solutions and applications : Lectures given at the 2nd session of the Centro Internazionale Matematico Estivo held in Montecatini Terme, Italy, June 1220, 1995
by
M Bardi(
Book
)
2 editions published in 1997 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1997 in English and held by 3 WorldCat member libraries worldwide
Wavefront propagation for reactiondiffusion systems of PDE
by G Barles(
Book
)
3 editions published in 1989 in English and held by 2 WorldCat member libraries worldwide
The theory of viscosity solutions for HamiltonJacobi equations is used to study the asymptotic behavior of solutions to certain systems of reactiondiffusion PDE. Our principal result characterizes the region of convergence of the solution to an unstable rest point as the set where the solution of an appropriate HamiltonJacobi equation is positive. Keywords include: Partial differential equations; Wavefront propagation
3 editions published in 1989 in English and held by 2 WorldCat member libraries worldwide
The theory of viscosity solutions for HamiltonJacobi equations is used to study the asymptotic behavior of solutions to certain systems of reactiondiffusion PDE. Our principal result characterizes the region of convergence of the solution to an unstable rest point as the set where the solution of an appropriate HamiltonJacobi equation is positive. Keywords include: Partial differential equations; Wavefront propagation
Differential Games and Representation Formulas for Solutions of HamiltonJacobiIsaacs Equations
by United States(
Book
)
2 editions published in 1983 in English and held by 2 WorldCat member libraries worldwide
Recent work by the authors and others has demonstrated the connections between the dynamic programming approach for twoperson, zerosum differential games and the new notion of viscosity solutions of HamiltonJacobi PDE, (Partial Differential Equations). The basic idea is that the dynamic programming optimality conditions imply that the values of a twoperson, zerosum differential game are viscosity solutions of appropriate PDE. This paper proves the above, when the values of the differential games are defined following ElliottKalton. This results in a great simplification in the statements and proofs, as the definitions are explicit and do not entail any kind of approximations. Moreover, as an application of the above results, the paper contains a representation formula for the solution of a fully nonlinear firstorder PDE. This is then used to prove results about the level sets of solutions of HamiltonJacobi equations with homogeneous Hamiltonians. These results are also related to the theory of Huygen's principle and geometric optics
2 editions published in 1983 in English and held by 2 WorldCat member libraries worldwide
Recent work by the authors and others has demonstrated the connections between the dynamic programming approach for twoperson, zerosum differential games and the new notion of viscosity solutions of HamiltonJacobi PDE, (Partial Differential Equations). The basic idea is that the dynamic programming optimality conditions imply that the values of a twoperson, zerosum differential game are viscosity solutions of appropriate PDE. This paper proves the above, when the values of the differential games are defined following ElliottKalton. This results in a great simplification in the statements and proofs, as the definitions are explicit and do not entail any kind of approximations. Moreover, as an application of the above results, the paper contains a representation formula for the solution of a fully nonlinear firstorder PDE. This is then used to prove results about the level sets of solutions of HamiltonJacobi equations with homogeneous Hamiltonians. These results are also related to the theory of Huygen's principle and geometric optics
Some Properties of Viscosity Solutions of HamiltonJacobi Equations
by
Mathematics Research Center (United States. Army)(
Book
)
2 editions published in 1982 in English and held by 2 WorldCat member libraries worldwide
Recently M.G. Crandall and P.L. Lions introduced the notion of 'viscosity solutions' of scalar nonlinear first order partial differential equations. Viscosity solutions need not be differentiable anywhere and thus are not sensitive to the classical problem of the crossing of characteristics. The value of this concept is established by the fact that very general existence, uniqueness and continuous dependence results hold for viscosity solutions of many problems arising in fields of application. The notion of a 'viscosity solution' admits several equivalent formulations. Here we look more closely at two of these equivalent criteria and exhibit their virtues by both proving several new facts and reproving various known results in a simpler manner. Moreover, by forsaking technical generality we hereby provide a more congenial introduction to this subject than the original paper. (Author)
2 editions published in 1982 in English and held by 2 WorldCat member libraries worldwide
Recently M.G. Crandall and P.L. Lions introduced the notion of 'viscosity solutions' of scalar nonlinear first order partial differential equations. Viscosity solutions need not be differentiable anywhere and thus are not sensitive to the classical problem of the crossing of characteristics. The value of this concept is established by the fact that very general existence, uniqueness and continuous dependence results hold for viscosity solutions of many problems arising in fields of application. The notion of a 'viscosity solution' admits several equivalent formulations. Here we look more closely at two of these equivalent criteria and exhibit their virtues by both proving several new facts and reproving various known results in a simpler manner. Moreover, by forsaking technical generality we hereby provide a more congenial introduction to this subject than the original paper. (Author)
A variational inequality approch to the BellmanDirichlet equation for two elliptic operators
by
H Brézis(
Book
)
2 editions published in 1977 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1977 in English and held by 2 WorldCat member libraries worldwide
Recent advances in nonlinear elliptic and parabolic problems : proceedings of an international conference, Nancy, France, March 1988
by Recent Advances in Nonlinear Elliptic and Parabolic Problems(
Book
)
1 edition published in 1989 in English and held by 1 WorldCat member library worldwide
1 edition published in 1989 in English and held by 1 WorldCat member library worldwide
A free boundary problem
by
Lawrence C Evans(
Book
)
1 edition published in 1975 in English and held by 1 WorldCat member library worldwide
1 edition published in 1975 in English and held by 1 WorldCat member library worldwide
A singular semilinear equation in $ L 1(R) $
by
Michael G Crandall(
Book
)
1 edition published in 1975 in English and held by 1 WorldCat member library worldwide
1 edition published in 1975 in English and held by 1 WorldCat member library worldwide
Hardy spaces and the twodimensional Euler equations with nonnegative vorticity
by
Lawrence C Evans(
Book
)
1 edition published in 1992 in English and held by 1 WorldCat member library worldwide
1 edition published in 1992 in English and held by 1 WorldCat member library worldwide
The remote sensing of Saturn's rings : I: The magnetic alinement of the ring particles
by
Lawrence Curtis Evans(
Book
)
1 edition published in 1973 in English and held by 1 WorldCat member library worldwide
Because of the potential implications for the optical properties of Saturn's rings, the orientation of nonspherical ring particles at equilibrium is investigated with respect to four stochastic influences: interactions with the interplanetary medium, interactions with the expected magnetic field of Saturn, thermal fluctuations due to the internal temperature of the ring particles; collisions between ring particles. The solution of the homogeneous FokkerPlanck equation for nearly spherical spheroids is presented and investigated in general. Values of the pertinent physical parameters in the vicinity of Saturn are estimated, and the implications for the alignment of the ring particles are investigated. It is concluded that for some alignment mechanisms, small ring particles can be expected to be almost completely aligned. This alignment results in each particle spinning around its shortest body axis with this axis parallel to the magnetic field direction (perpendicular to the ring plane)
1 edition published in 1973 in English and held by 1 WorldCat member library worldwide
Because of the potential implications for the optical properties of Saturn's rings, the orientation of nonspherical ring particles at equilibrium is investigated with respect to four stochastic influences: interactions with the interplanetary medium, interactions with the expected magnetic field of Saturn, thermal fluctuations due to the internal temperature of the ring particles; collisions between ring particles. The solution of the homogeneous FokkerPlanck equation for nearly spherical spheroids is presented and investigated in general. Values of the pertinent physical parameters in the vicinity of Saturn are estimated, and the implications for the alignment of the ring particles are investigated. It is concluded that for some alignment mechanisms, small ring particles can be expected to be almost completely aligned. This alignment results in each particle spinning around its shortest body axis with this axis parallel to the magnetic field direction (perpendicular to the ring plane)
Nonlinear evolution equations in Banach spaces
by
Lawrence C Evans(
Book
)
1 edition published in 1975 in English and held by 1 WorldCat member library worldwide
1 edition published in 1975 in English and held by 1 WorldCat member library worldwide
On the Relation of the Operator Partial derivative with respect to s + Partial derivative with respect to tau to Evolution Governed by Accretive Operators
(
Book
)
1 edition published in 1975 in English and held by 1 WorldCat member library worldwide
Existence theorems for the equation du/dt + Au = f(t), where A is an accretive operator in a general Banach space X, are typically proved by showing that limits of solutions of discrete approximations to the equation exist. Here the estimates required to show this convergence are exhibited as special cases of estimates relating solutions of difference schemes for partial derivative with respect to s + partial derivative with respect to tau to exact solutions
1 edition published in 1975 in English and held by 1 WorldCat member library worldwide
Existence theorems for the equation du/dt + Au = f(t), where A is an accretive operator in a general Banach space X, are typically proved by showing that limits of solutions of discrete approximations to the equation exist. Here the estimates required to show this convergence are exhibited as special cases of estimates relating solutions of difference schemes for partial derivative with respect to s + partial derivative with respect to tau to exact solutions
I cannot go back
by
L. C Evans(
)
1 edition published in 2010 in English and held by 1 WorldCat member library worldwide
1 edition published in 2010 in English and held by 1 WorldCat member library worldwide
Military and imperial organization : notes for Certificate "B" and promotion
by
L. C Evans(
Book
)
1 edition published in 1935 in English and held by 1 WorldCat member library worldwide
1 edition published in 1935 in English and held by 1 WorldCat member library worldwide
A PDE approach to geometric optics for certain semilinear parabolic equations
by
L. C Evans(
Book
)
2 editions published in 1987 in English and held by 1 WorldCat member library worldwide
2 editions published in 1987 in English and held by 1 WorldCat member library worldwide
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Associated Subjects
Approximation theory ArmiesOrganization Banach spaces Boundary value problems Cauchy problem Convergence Curvature Difference equations Differential equations, Elliptic Differential equations, Nonlinear Differential equations, Parabolic Differential equations, Partial Differential operators Evolution equations Existence theorems Faith Great Britain HamiltonJacobi equations Military education Monotone operators Phase transformations (Statistical physics) Reactiondiffusion equations Saturn (Planet) Viscosity solutions Wave equation