Ni, W.M (WeiMing)
Overview
Works:  20 works in 86 publications in 4 languages and 892 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Other 
Classifications:  QA377, 515.353 
Publication Timeline
.
Most widely held works by
W.M Ni
Nonlinear diffusion equations and their equilibrium states : proceedings of a microprogram held August 25September 12, 1986 by
W.M Ni(
Book
)
10 editions published in 1988 in English and held by 196 WorldCat member libraries worldwide
10 editions published in 1988 in English and held by 196 WorldCat member libraries worldwide
The mathematics of diffusion by
W.M Ni(
Book
)
12 editions published in 2011 in English and held by 182 WorldCat member libraries worldwide
Diffusion has been used extensively in many scientific disciplines to model a wide variety of phenomena. The Mathematics of Diffusion focuses on the qualitative properties of solutions to nonlinear elliptic and parabolic equations and systems in connection with domain geometry, various boundary conditions, the mechanism of different diffusion rates, and the interaction between diffusion and spatial heterogeneity. The book systematically explores the interplay between different diffusion rates from the viewpoint of pattern formation, particularly Turing's diffusiondriven instability in both homogeneous and heterogeneous environments, and the roles of random diffusion, directed movements, and spatial heterogeneity in the classical LotkaVolterra competition systems. Interspersed throughout the book are many simple, fundamental, and important open problems for readers to investigate
12 editions published in 2011 in English and held by 182 WorldCat member libraries worldwide
Diffusion has been used extensively in many scientific disciplines to model a wide variety of phenomena. The Mathematics of Diffusion focuses on the qualitative properties of solutions to nonlinear elliptic and parabolic equations and systems in connection with domain geometry, various boundary conditions, the mechanism of different diffusion rates, and the interaction between diffusion and spatial heterogeneity. The book systematically explores the interplay between different diffusion rates from the viewpoint of pattern formation, particularly Turing's diffusiondriven instability in both homogeneous and heterogeneous environments, and the roles of random diffusion, directed movements, and spatial heterogeneity in the classical LotkaVolterra competition systems. Interspersed throughout the book are many simple, fundamental, and important open problems for readers to investigate
Degenerate diffusions by
W.M Ni(
Book
)
15 editions published between 1992 and 1993 in English and German and held by 177 WorldCat member libraries worldwide
This volume is the proceedings of the IMA workshop "Degenerate Diffusions" held at the University of Minnesota from May 13May 18, 1991. The workshop consisted of two parts. The emphasis of the first four days was on current progress or new problems in nonlinear diffusions involving free boundaries or sharp interfaces. Analysts and geometers will find some of the mathematical models described in this volume interesting; and the papers of more pure mathematical nature included here should provide applied mathematicians with powerful methods and useful techniques in handling singular perturbation problems as well as free boundary problems. The last two days of the workshop were a celebration of James Serrin's 65th birthday. A wide range of topics was covered in this part of the workshop. As a consequence, the scope of this book is much broader than what the title Degenerate Diffusions might suggest
15 editions published between 1992 and 1993 in English and German and held by 177 WorldCat member libraries worldwide
This volume is the proceedings of the IMA workshop "Degenerate Diffusions" held at the University of Minnesota from May 13May 18, 1991. The workshop consisted of two parts. The emphasis of the first four days was on current progress or new problems in nonlinear diffusions involving free boundaries or sharp interfaces. Analysts and geometers will find some of the mathematical models described in this volume interesting; and the papers of more pure mathematical nature included here should provide applied mathematicians with powerful methods and useful techniques in handling singular perturbation problems as well as free boundary problems. The last two days of the workshop were a celebration of James Serrin's 65th birthday. A wide range of topics was covered in this part of the workshop. As a consequence, the scope of this book is much broader than what the title Degenerate Diffusions might suggest
Nonlinear diffusion equations and their equilibrium states II : proceedings of a microprogram held August 25  September 12,
1986 by
W.M Ni(
Book
)
10 editions published in 1988 in English and held by 29 WorldCat member libraries worldwide
In recent years considerable interest has been focused on nonlinear diffu sion problems, the archetypical equation for these being Ut = ~U + f(u). Here ~ denotes the ndimensional Laplacian, the solution u = u(x, t) is defined over some spacetime domain of the form n x [O, T], and f(u) is a given real function whose form is determined by various physical and mathematical applications. These applications have become more varied and widespread as problem after problem has been shown to lead to an equation of this type or to its timeindependent counterpart, the elliptic equation of equilibrium ~u+f(u)=O. Particular cases arise, for example, in population genetics, the physics of nu clear stability, phase transitions between liquids and gases, flows in porous media, the LendEmden equation of astrophysics, various simplified com bustion models, and in determining metrics which realize given scalar or Gaussian curvatures. In the latter direction, for example, the problem of finding conformal metrics with prescribed curvature leads to a ground state problem involving critical exponents. Thus not only analysts, but geome ters as well, can find common ground in the present work. The corresponding mathematical problem is to determine how the struc ture of the nonlinear function f(u) influences the behavior of the solution
10 editions published in 1988 in English and held by 29 WorldCat member libraries worldwide
In recent years considerable interest has been focused on nonlinear diffu sion problems, the archetypical equation for these being Ut = ~U + f(u). Here ~ denotes the ndimensional Laplacian, the solution u = u(x, t) is defined over some spacetime domain of the form n x [O, T], and f(u) is a given real function whose form is determined by various physical and mathematical applications. These applications have become more varied and widespread as problem after problem has been shown to lead to an equation of this type or to its timeindependent counterpart, the elliptic equation of equilibrium ~u+f(u)=O. Particular cases arise, for example, in population genetics, the physics of nu clear stability, phase transitions between liquids and gases, flows in porous media, the LendEmden equation of astrophysics, various simplified com bustion models, and in determining metrics which realize given scalar or Gaussian curvatures. In the latter direction, for example, the problem of finding conformal metrics with prescribed curvature leads to a ground state problem involving critical exponents. Thus not only analysts, but geome ters as well, can find common ground in the present work. The corresponding mathematical problem is to determine how the struc ture of the nonlinear function f(u) influences the behavior of the solution
Nonlinear diffusion equations and their equilibrium states I : proceedings of a microprogram held August 25  September 12,
1986 by
W.M Ni(
Book
)
10 editions published in 1988 in English and Italian and held by 28 WorldCat member libraries worldwide
In recent years considerable interest has been focused on nonlinear diffu sion problems, the archetypical equation for these being Ut = D.u + f(u). Here D. denotes the ndimensional Laplacian, the solution u = u(x, t) is defined over some spacetime domain of the form n x [O,T], and f(u) is a given real function whose form is determined by various physical and mathematical applications. These applications have become more varied and widespread as problem after problem has been shown to lead to an equation of this type or to its timeindependent counterpart, the elliptic equation of equilibrium D.u + f(u) = o. Particular cases arise, for example, in population genetics, the physics of nu clear stability, phase transitions between liquids and gases, flows in porous media, the LendEmden equation of astrophysics, various simplified com bustion models, and in determining metrics which realize given scalar or Gaussian curvatures. In the latter direction, for example, the problem of finding conformal metrics with prescribed curvature leads to a ground state problem involving critical exponents. Thus not only analysts, but geome ters as well, can find common ground in the present work. The corresponding mathematical problem is to determine how the struc ture of the nonlinear function f(u) influences the behavior of the solution
10 editions published in 1988 in English and Italian and held by 28 WorldCat member libraries worldwide
In recent years considerable interest has been focused on nonlinear diffu sion problems, the archetypical equation for these being Ut = D.u + f(u). Here D. denotes the ndimensional Laplacian, the solution u = u(x, t) is defined over some spacetime domain of the form n x [O,T], and f(u) is a given real function whose form is determined by various physical and mathematical applications. These applications have become more varied and widespread as problem after problem has been shown to lead to an equation of this type or to its timeindependent counterpart, the elliptic equation of equilibrium D.u + f(u) = o. Particular cases arise, for example, in population genetics, the physics of nu clear stability, phase transitions between liquids and gases, flows in porous media, the LendEmden equation of astrophysics, various simplified com bustion models, and in determining metrics which realize given scalar or Gaussian curvatures. In the latter direction, for example, the problem of finding conformal metrics with prescribed curvature leads to a ground state problem involving critical exponents. Thus not only analysts, but geome ters as well, can find common ground in the present work. The corresponding mathematical problem is to determine how the struc ture of the nonlinear function f(u) influences the behavior of the solution
Proceedings of a microprogram held August 25  September 12, 1986 : W.M. Ni ; L.A. Peletier ; J. Serrin, eds(
Book
)
2 editions published in 1988 in English and held by 15 WorldCat member libraries worldwide
2 editions published in 1988 in English and held by 15 WorldCat member libraries worldwide
Nonlinear diffusion equations and their equilibrium states, 3 : proceedings from a conference held August 2029, 1989, in
Gregynog, Wales by
H Brézis(
Book
)
7 editions published in 1992 in English and held by 10 WorldCat member libraries worldwide
Nonlinear diffusion equations have held a prominent place in the theory of partial differential equations, both for the challenging and deep math ematical questions posed by such equations and the important role they play in many areas of science and technology. Examples of current inter est are biological and chemical pattern formation, semiconductor design, environmental problems such as solute transport in groundwater flow, phase transitions and combustion theory. Central to the theory is the equation Ut = ~cp(U) + f(u). Here ~ denotes the ndimensional Laplacian, cp and f are given functions and the solution is defined on some domain n x [0, T] in spacetime. FUn damental questions concern the existence, uniqueness and regularity of so lutions, the existence of interfaces or free boundaries, the question as to whether or not the solution can be continued for all time, the asymptotic behavior, both in time and space, and the development of singularities, for instance when the solution ceases to exist after finite time, either through extinction or through blow up
7 editions published in 1992 in English and held by 10 WorldCat member libraries worldwide
Nonlinear diffusion equations have held a prominent place in the theory of partial differential equations, both for the challenging and deep math ematical questions posed by such equations and the important role they play in many areas of science and technology. Examples of current inter est are biological and chemical pattern formation, semiconductor design, environmental problems such as solute transport in groundwater flow, phase transitions and combustion theory. Central to the theory is the equation Ut = ~cp(U) + f(u). Here ~ denotes the ndimensional Laplacian, cp and f are given functions and the solution is defined on some domain n x [0, T] in spacetime. FUn damental questions concern the existence, uniqueness and regularity of so lutions, the existence of interfaces or free boundaries, the question as to whether or not the solution can be continued for all time, the asymptotic behavior, both in time and space, and the development of singularities, for instance when the solution ceases to exist after finite time, either through extinction or through blow up
Nonlinear diffusion equations and their equilibrium states(
Book
)
1 edition published in 1988 in English and held by 7 WorldCat member libraries worldwide
1 edition published in 1988 in English and held by 7 WorldCat member libraries worldwide
Nonlinear diffusion equations and their equilibrium states(
Book
)
1 edition published in 1988 in English and held by 7 WorldCat member libraries worldwide
1 edition published in 1988 in English and held by 7 WorldCat member libraries worldwide
A counterexample to the Nodal Domain Conjecture and a related semilinear equation* by
ChangShou Lin(
Book
)
2 editions published in 1986 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1986 in English and held by 3 WorldCat member libraries worldwide
Spikelayers in semilinear elliptic singular perturbation problems by
W.M Ni(
Book
)
2 editions published in 1992 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1992 in English and held by 2 WorldCat member libraries worldwide
Convegno su partial differential equations and geometry by Convegno su Partial Differential Equations and Geometry(
Book
)
1 edition published in 1989 in Italian and held by 2 WorldCat member libraries worldwide
1 edition published in 1989 in Italian and held by 2 WorldCat member libraries worldwide
Nonlinear Diffusion Equations and Their Equilibrium : States : Vol.: 1 : Proceedings of a Microprogram held August 25  :
September 12, 1986(
Book
)
2 editions published in 1988 in Undetermined and held by 2 WorldCat member libraries worldwide
2 editions published in 1988 in Undetermined and held by 2 WorldCat member libraries worldwide
On the elliptic equation Luk + Ke 2U = 0 by
Carlos E Kenig(
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
Some minimax principles with applications in non linear elliptic boundary value problems and global vortex flow by
W.M Ni(
Book
)
3 editions published in 1979 in English and held by 2 WorldCat member libraries worldwide
3 editions published in 1979 in English and held by 2 WorldCat member libraries worldwide
Nonlinear diffusion equations and their equilibrium states : Microprogram : Papers(
)
1 edition published in 1988 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1988 in English and held by 2 WorldCat member libraries worldwide
On diffusioninduced blowups in a cooperative model by
Calif.) Mathematical Sciences Research Institute (Berkeley(
Book
)
1 edition published in 1996 in English and held by 1 WorldCat member library worldwide
1 edition published in 1996 in English and held by 1 WorldCat member library worldwide
Kong shou dao ji fa by
W.M Ni(
)
1 edition published in 2006 in Chinese and held by 1 WorldCat member library worldwide
1 edition published in 2006 in Chinese and held by 1 WorldCat member library worldwide
Zhong kao shi fen 1000 ge wei shen me(
Book
)
1 edition published in 1997 in Chinese and held by 1 WorldCat member library worldwide
1 edition published in 1997 in Chinese and held by 1 WorldCat member library worldwide
Mei wen jie jian ci dian(
Book
)
1 edition published in 2001 in Chinese and held by 1 WorldCat member library worldwide
1 edition published in 2001 in Chinese and held by 1 WorldCat member library worldwide
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Audience Level
0 

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Kids  General  Special 
Related Identities
 Peletier, L. A. (Lambertus A.) Editor
 Serrin, J. (James) 19262012 Editor
 Vazquez, J. L. (Juan Luis) Editor
 Society for Industrial and Applied Mathematics
 Mathematical Sciences Research Institute (Berkeley, Calif.) Editor
 Lloyd, N. G.
 Brezis, Haim Author
 Serrin (1926 ) (James) Editor
 Friedman, Avner Author
 Peletier (Lambertus A.). Editor
Associated Subjects
Boundary value problems Differentiable dynamical systems Differential equations Differential equations, Nonlinear Differential equations, Partial Diffusion DiffusionMathematical models Geometry, Differential Global analysis (Mathematics) Heat equation Mathematics Perturbation (Mathematics) Reactiondiffusion equations