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Nonlinear Diffusion Equations And Their Equilibrium States Ii
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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.
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.
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 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
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.
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:
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.
Book Synopsis Nonlinear Diffusion Equations and Their Equilibrium States II. by : Wei-Ming Ni
Download or read book Nonlinear Diffusion Equations and Their Equilibrium States II. written by Wei-Ming Ni and published by . This book was released on 1988-01 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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:
Book Synopsis Nonlinear Diffusion Equations and Their Equilibrium by : W.-M. Ni
Download or read book Nonlinear Diffusion Equations and Their Equilibrium written by W.-M. Ni and published by . This book was released on 1988 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
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:
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:
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:
Book Synopsis Nonlinear Diffusion Equations and Their Equilibrium by : W.-M. Ni
Download or read book Nonlinear Diffusion Equations and Their Equilibrium written by W.-M. Ni and published by . This book was released on 1988 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Nonlinear diffusion equations and their equilibrium states by : N. G. Lloyd
Download or read book Nonlinear diffusion equations and their equilibrium states written by N. G. Lloyd and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
