Nonlinear Diffusion Equations And Their Equilibrium States I

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Nonlinear Diffusion Equations and Their Equilibrium States I

Author : W.-M. Ni
Publisher : Springer Science & Business Media
ISBN 13 : 1461396050
Total Pages : 359 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Nonlinear Diffusion Equations and Their Equilibrium States I by : W.-M. Ni

Download or read book Nonlinear Diffusion Equations and Their Equilibrium States I written by W.-M. Ni and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 n-dimensional Laplacian, the solution u = u(x, t) is defined over some space-time 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 time-independent 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 Lend-Emden 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, 3

Author : N.G Lloyd
Publisher : Springer Science & Business Media
ISBN 13 : 1461203937
Total Pages : 567 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Nonlinear Diffusion Equations and Their Equilibrium States, 3 by : N.G Lloyd

Download or read book Nonlinear Diffusion Equations and Their Equilibrium States, 3 written by N.G Lloyd and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 567 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 n-dimensional Laplacian, cp and f are given functions and the solution is defined on some domain n x [0, T] in space-time. 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 I

Author : W.-M. Ni
Publisher : Springer
ISBN 13 :
Total Pages : 384 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Nonlinear Diffusion Equations and Their Equilibrium States I by : W.-M. Ni

Download or read book Nonlinear Diffusion Equations and Their Equilibrium States I written by W.-M. Ni and published by Springer. This book was released on 1988-06-24 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 n-dimensional Laplacian, the solution u = u(x, t) is defined over some space-time 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 time-independent 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 Lend-Emden 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 II

Author : W.-M. Ni
Publisher : Springer Science & Business Media
ISBN 13 : 1461396085
Total Pages : 364 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Nonlinear Diffusion Equations and Their Equilibrium States II by : W.-M. Ni

Download or read book Nonlinear Diffusion Equations and Their Equilibrium States II written by W.-M. Ni and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 n-dimensional Laplacian, the solution u = u(x, t) is defined over some space-time 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 time-independent 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 Lend-Emden 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

Author :
Publisher :
ISBN 13 : 9783540967712
Total Pages : 0 pages
Book Rating : 4.9/5 (677 download)

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Book Synopsis Nonlinear Diffusion Equations and Their Equilibrium States by :

Download or read book Nonlinear Diffusion Equations and Their Equilibrium States written by and published by . This book was released on 1988 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nonlinear Diffusion Equations and Their Equilibrium States II

Author : W.-M. Ni
Publisher : Springer
ISBN 13 :
Total Pages : 392 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Nonlinear Diffusion Equations and Their Equilibrium States II by : W.-M. Ni

Download or read book Nonlinear Diffusion Equations and Their Equilibrium States II written by W.-M. Ni and published by Springer. This book was released on 1988-06-24 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 n-dimensional Laplacian, the solution u = u(x, t) is defined over some space-time 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 time-independent 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 Lend-Emden 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, 3

Author : N. G. Lloyd
Publisher : Birkhauser
ISBN 13 : 9783764335311
Total Pages : 572 pages
Book Rating : 4.3/5 (353 download)

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Book Synopsis Nonlinear Diffusion Equations and Their Equilibrium States, 3 by : N. G. Lloyd

Download or read book Nonlinear Diffusion Equations and Their Equilibrium States, 3 written by N. G. Lloyd and published by Birkhauser. This book was released on 1992-01-01 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nonlinear Diffusion Equations and Their Equilibrium States

Author :
Publisher :
ISBN 13 : 9783764335311
Total Pages : pages
Book Rating : 4.3/5 (353 download)

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Book Synopsis Nonlinear Diffusion Equations and Their Equilibrium States by :

Download or read book Nonlinear Diffusion Equations and Their Equilibrium States written by and published by . This book was released on 1992 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nonlinear Diffusion Equations and Their Equilibrium States

Author :
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (88 download)

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Book Synopsis Nonlinear Diffusion Equations and Their Equilibrium States by :

Download or read book Nonlinear Diffusion Equations and Their Equilibrium States written by and published by . This book was released on 1988 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nonlinear Diffusion Equations and Their Equilibrium States II

Author :
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (277 download)

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Book Synopsis Nonlinear Diffusion Equations and Their Equilibrium States II by :

Download or read book Nonlinear Diffusion Equations and Their Equilibrium States II written by and published by . This book was released on 1988 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nonlinear Diffusion Equations

Author : Zhuoqun Wu
Publisher : World Scientific
ISBN 13 : 9789812799791
Total Pages : 526 pages
Book Rating : 4.7/5 (997 download)

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Book Synopsis Nonlinear Diffusion Equations by : Zhuoqun Wu

Download or read book Nonlinear Diffusion Equations written by Zhuoqun Wu and published by World Scientific. This book was released on 2001 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear diffusion equations, an important class of parabolic equations, come from a variety of diffusion phenomena which appear widely in nature. They are suggested as mathematical models of physical problems in many fields, such as filtration, phase transition, biochemistry and dynamics of biological groups. In many cases, the equations possess degeneracy or singularity. The appearance of degeneracy or singularity makes the study more involved and challenging. Many new ideas and methods have been developed to overcome the special difficulties caused by the degeneracy and singularity, which enrich the theory of partial differential equations. This book provides a comprehensive presentation of the basic problems, main results and typical methods for nonlinear diffusion equations with degeneracy. Some results for equations with singularity are touched upon. Contents: Newtonian Filtration Equations: Existence and Uniqueness of Solutions: One Dimensional Case; Existence and Uniqueness of Solutions: Higher Dimensional Case; Regularity of Solutions: One Dimensional Case; Regularity of Solutions: Higher Dimensional Case; Properties of the Free Boundary: One Dimensional Case; Properties of the Free Boundary: Higher Dimensional Case; Initial Trace of Solutions; Other Problems; Non-Newtonian Filtration Equations: Existence of Solutions; Harnack Inequality and Initial Trace of Solutions; Regularity of Solutions; Uniqueness of Solutions; Properties of the Free Boundary; Other Problems; General Quasilinear Equations of Second Order: Weakly Degenerate Equations in One Dimension; Weakly Degenerate Equations in Higher Dimension; Strongly Degenerate Equations in One Dimension; Degenerate Equations in Higher Dimension without Terms of Lower Order; General Strongly Degenerate Equations in Higher Dimension; Classes BV and BV x; Nonlinear Diffusion Equations of Higher Order: Similarity Solutions of a Fourth Order Equation; Equations with Double-Degeneracy; CahnOCoHilliard Equation with Constant Mobility; CahnOCoHilliard Equations with Positive Concentration Dependent Mobility; Thin Film Equation; CahnOCoHilliard Equation with Degenerate Mobility. Readership: Researchers, lecturers and graduate students in the fields of analysis and differential equations, mathematical physics and fluid mechanics."

Dual Variational Approach to Nonlinear Diffusion Equations

Author : Gabriela Marinoschi
Publisher : Springer Nature
ISBN 13 : 3031245830
Total Pages : 223 pages
Book Rating : 4.0/5 (312 download)

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Book Synopsis Dual Variational Approach to Nonlinear Diffusion Equations by : Gabriela Marinoschi

Download or read book Dual Variational Approach to Nonlinear Diffusion Equations written by Gabriela Marinoschi and published by Springer Nature. This book was released on 2023-03-28 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph explores a dual variational formulation of solutions to nonlinear diffusion equations with general nonlinearities as null minimizers of appropriate energy functionals. The author demonstrates how this method can be utilized as a convenient tool for proving the existence of these solutions when others may fail, such as in cases of evolution equations with nonautonomous operators, with low regular data, or with singular diffusion coefficients. By reducing it to a minimization problem, the original problem is transformed into an optimal control problem with a linear state equation. This procedure simplifies the proof of the existence of minimizers and, in particular, the determination of the first-order conditions of optimality. The dual variational formulation is illustrated in the text with specific diffusion equations that have general nonlinearities provided by potentials having various stronger or weaker properties. These equations can represent mathematical models to various real-world physical processes. Inverse problems and optimal control problems are also considered, as this technique is useful in their treatment as well.

Evolution Equations and Lagrangian Coordinates

Author : Anvarbek M. Meirmanov
Publisher : Walter de Gruyter
ISBN 13 : 311087444X
Total Pages : 329 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Evolution Equations and Lagrangian Coordinates by : Anvarbek M. Meirmanov

Download or read book Evolution Equations and Lagrangian Coordinates written by Anvarbek M. Meirmanov and published by Walter de Gruyter. This book was released on 2011-07-20 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich and Z. Janko, Groups of Prime Power Order, Volume 6 (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

Classification of Radial Solutions Arising in the Study of Thermal Structures with Thermal Equilibrium or No Flux at the Boundary

Author : Alfonso Castro
Publisher : American Mathematical Soc.
ISBN 13 : 0821847260
Total Pages : 87 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Classification of Radial Solutions Arising in the Study of Thermal Structures with Thermal Equilibrium or No Flux at the Boundary by : Alfonso Castro

Download or read book Classification of Radial Solutions Arising in the Study of Thermal Structures with Thermal Equilibrium or No Flux at the Boundary written by Alfonso Castro and published by American Mathematical Soc.. This book was released on 2010 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors provide a complete classification of the radial solutions to a class of reaction diffusion equations arising in the study of thermal structures such as plasmas with thermal equilibrium or no flux at the boundary. In particular, their study includes rapidly growing nonlinearities, that is, those where an exponent exceeds the critical exponent. They describe the corresponding bifurcation diagrams and determine existence and uniqueness of ground states, which play a central role in characterizing those diagrams. They also provide information on the stability-unstability of the radial steady states.

Travelling Waves in Nonlinear Diffusion-Convection Reaction

Author : Brian H. Gilding
Publisher : Birkhäuser
ISBN 13 : 3034879644
Total Pages : 214 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Travelling Waves in Nonlinear Diffusion-Convection Reaction by : Brian H. Gilding

Download or read book Travelling Waves in Nonlinear Diffusion-Convection Reaction written by Brian H. Gilding and published by Birkhäuser. This book was released on 2012-12-06 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph has grown out of research we started in 1987, although the foun dations were laid in the 1970's when both of us were working on our doctoral theses, trying to generalize the now classic paper of Oleinik, Kalashnikov and Chzhou on nonlinear degenerate diffusion. Brian worked under the guidance of Bert Peletier at the University of Sussex in Brighton, England, and, later at Delft University of Technology in the Netherlands on extending the earlier mathematics to include nonlinear convection; while Robert worked at Lomonosov State Univer sity in Moscow under the supervision of Anatolii Kalashnikov on generalizing the earlier mathematics to include nonlinear absorption. We first met at a conference held in Rome in 1985. In 1987 we met again in Madrid at the invitation of Ildefonso Diaz, where we were both staying at 'La Residencia'. As providence would have it, the University 'Complutense' closed down during this visit in response to student demonstra tions, and, we were very much left to our own devices. It was natural that we should gravitate to a research topic of common interest. This turned out to be the characterization of the phenomenon of finite speed of propagation for nonlin ear reaction-convection-diffusion equations. Brian had just completed some work on this topic for nonlinear diffusion-convection, while Robert had earlier done the same for nonlinear diffusion-absorption. There was no question but that we bundle our efforts on the general situation.

Semigroup Approach To Nonlinear Diffusion Equations

Author : Viorel Barbu
Publisher : World Scientific
ISBN 13 : 981124653X
Total Pages : 221 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Semigroup Approach To Nonlinear Diffusion Equations by : Viorel Barbu

Download or read book Semigroup Approach To Nonlinear Diffusion Equations written by Viorel Barbu and published by World Scientific. This book was released on 2021-09-23 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is concerned with functional methods (nonlinear semigroups of contractions, nonlinear m-accretive operators and variational techniques) in the theory of nonlinear partial differential equations of elliptic and parabolic type. In particular, applications to the existence theory of nonlinear parabolic equations, nonlinear Fokker-Planck equations, phase transition and free boundary problems are presented in details. Emphasis is put on functional methods in partial differential equations (PDE) and less on specific results.

Convex Analysis and Nonlinear Geometric Elliptic Equations

Author : Ilya J. Bakelman
Publisher : Springer Science & Business Media
ISBN 13 : 3642698816
Total Pages : 524 pages
Book Rating : 4.6/5 (426 download)

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Book Synopsis Convex Analysis and Nonlinear Geometric Elliptic Equations by : Ilya J. Bakelman

Download or read book Convex Analysis and Nonlinear Geometric Elliptic Equations written by Ilya J. Bakelman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: Investigations in modem nonlinear analysis rely on ideas, methods and prob lems from various fields of mathematics, mechanics, physics and other applied sciences. In the second half of the twentieth century many prominent, ex emplary problems in nonlinear analysis were subject to intensive study and examination. The united ideas and methods of differential geometry, topology, differential equations and functional analysis as well as other areas of research in mathematics were successfully applied towards the complete solution of com plex problems in nonlinear analysis. It is not possible to encompass in the scope of one book all concepts, ideas, methods and results related to nonlinear analysis. Therefore, we shall restrict ourselves in this monograph to nonlinear elliptic boundary value problems as well as global geometric problems. In order that we may examine these prob lems, we are provided with a fundamental vehicle: The theory of convex bodies and hypersurfaces. In this book we systematically present a series of centrally significant results obtained in the second half of the twentieth century up to the present time. Particular attention is given to profound interconnections between various divisions in nonlinear analysis. The theory of convex functions and bodies plays a crucial role because the ellipticity of differential equations is closely connected with the local and global convexity properties of their solutions. Therefore it is necessary to have a sufficiently large amount of material devoted to the theory of convex bodies and functions and their connections with partial differential equations.