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Sunday, May 10, 2020 | History

4 edition of **Nonlinear Diffusion Equations and Their Equilibrium States, 3** found in the catalog.

Nonlinear Diffusion Equations and Their Equilibrium States, 3

N. G. Lloyd

- 213 Want to read
- 34 Currently reading

Published
**January 1992**
by Birkhauser
.

Written in English

- Differential Equations - Partial Differential Equations,
- Mathematics

The Physical Object | |
---|---|

Format | Hardcover |

Number of Pages | 572 |

ID Numbers | |

Open Library | OL9090142M |

ISBN 10 | 3764335319 |

ISBN 10 | 9783764335311 |

We investigate solutions of a generalized diffusion equation that contains nonlinear terms in the presence of external forces and reaction terms. The solutions found here can have a compact or long tail behavior and can be expressed in terms of the q-exponential functions present in the Tsallis framework. In the case of the long-tailed behavior, in the asymptotic limit, these solutions can Cited by: 2. Linearization of Diﬀerential Equation Models 1 Motivation We cannot solve most nonlinear models, so we often instead try to get an overall feel for the way the model behaves: we sometimes talk about looking at the qualitative dynamics of a system. Equilibrium points– steady states of the system– are an important feature that we look for. ManyFile Size: KB.

Linearization of non-linear state equation rect mapping of the systems dynamics as well as their stability, [2,5,9]. The most common linearization method i.e. expansion in Taylor’s series around the equilibrium point is a very effective approximation of the. Nonlinear Diffusion Equations bistable transmission lines ], and is a degenerate case of the FITZHUGH- NAGUMO model for the propagation of nerve pulses (see also [18]). Finally, this case is also very relevant to models for pattern formation and wave propagation.

Thanks for contributing an answer to Mathematics Stack Exchange! Please be sure to answer the question. Provide details and share your research! But avoid Asking for help, clarification, or responding to other answers. Making statements based on opinion; back them up with references or personal experience. Use MathJax to format equations. University as being representative of a type of nonlinear diffusion problem for which there was not a satisfactory numerical method of solution. Existing methods, applicable to this problem, are of the implicit type and require the solution of an algebraic system, in most cases a nonlinear system, at each time level |l,3,^. In typical diffusionAuthor: Lonny Bee Winrich.

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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. 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.

Nonlinear Diffusion Equations and Their Equilibrium States II Proceedings of a Microprogram held August 25–Septem Editors: Ni, W.-M., Peletier, L.A. Get this from a library. Nonlinear diffusion equations and their equilibrium states, 3: proceedings from a conference held August, in Gregynog, Wales.

[N G Lloyd;]. Buy Nonlinear Diffusion Equations and Their Equilibrium States I: Proceedings of a Microprogram held August Septem (Mathematical Sciences Research Institute Publications (12)) on FREE SHIPPING on qualified ordersAuthor: W.-M. Ni L. Peletier.

Full Description: "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 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.

Burgers originally proposed equation (6) as a model for turbulence [2, 3] and it has found application in gas dynamics [5, 7] and acoustics [9], among other areas.

One of the earliest known solutions to Burgers’ equation is the Fourier series solution attributed to Fay ([6]). Get this from a library. Nonlinear Diffusion Equations and Their Equilibrium States I: Proceedings of a Microprogram held August Septem [W -M Ni; L A Peletier; James Serrin] -- In recent years considerable interest has been focused on nonlinear diffu sion problems, the archetypical equation for these being Ut = D.u + f(u).

Nonlinear Diffusion Equations and Their Equilibrium States I: Proceedings of a Microprogram Held August Septem by W.M. Ni (Editor), James Serrin (Editor)4/5(1). Nonlinear Diffusion These notes summarize the way I present this material, for my beneﬁt.

But everything in here is said in more detail, and better, in Weickert’s paper. 1 Introduction: Motivation for non-standard diffusion First, let’s begin with some deﬁnitions and examples of why we want to use other kinds of diffusionFile Size: 49KB.

Including the basic mathematical tools needed to understand the rules for operating with the fractional derivatives and fractional differential equations, this self-contained text presents the possibility of using fractional diffusion equations with anomalous diffusion phenomena to propose powerful mathematical models for a large variety of Cited by: Book Name Author(s) Ginzburg-Landau Vortices 0th Edition 0 Problems solved: HaÃ¯m Brezis, Tatsien Li, Haim Brezis, Daqian Li: Ginzburg-Landau Vortices 1st Edition 0 Problems solved: Frederic Helein, Fabrice Bethuel, Haim Brezis: Nonlinear Diffusion Equations and Their Equilibrium States, 3 0th Edition 0 Problems solved.

Nonlinear Diffusion Equations and Their Equilibrium States, 3, () Blow-up for semilinear parabolic equations with a gradient term. Mathematical Methods in the Applied SciencesCited by: Constrained problems for ordinary differential equations and their solution in the abstract setting of bifurcation theory continue to attract wide attention.

upper and lower bounds for the solutions of initial-boundary value problems associated with nonlinear reaction–diffusion equations. The nonlinear analysis approximation technique. The statistical theory described above provides a prediction for the expected value of the kinetic energy K n in statistical equilibrium for given number of modes is 〈K n 〉=K n (〈ψ (n) 〉)+H 0 −H n ∗, which follows directly upon multiplying Eq.

(22) by k j 2 and summing over first term in this expression for 〈K n 〉 is the contribution to the mean kinetic energy Cited by: 6. Chapter 8 The Reaction-Diffusion Equations Reaction-diffusion (RD) equations arise naturally in systems consisting of many interacting components, (e.g., chemical reactions) and are widely used to describe pattern-formation phenomena in variety of biological, chemical and physical sys-tems.

Saturation terms are added to the classical Volterra–Lotka model and to generalizations of it which maintain its qualitative character.

To describe the effect of migration, diffusion terms are intr Cited by: @article{osti_, title = {A moving mesh finite difference method for equilibrium radiation diffusion equations}, author = {Yang, Xiaobo and Huang, Weizhang and Qiu, Jianxian}, abstractNote = {An efficient moving mesh finite difference method is developed for the numerical solution of equilibrium radiation diffusion equations in two dimensions.

Diffusion is the net movement of anything (for example, atom, ions, molecules) from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in concentration. The concept of diffusion is widely used in many fields, including physics (particle diffusion), chemistry, biology, sociology, economics, and finance (diffusion of people, ideas, and price.

The stationary states of diffusion belong to an important world,elliptic equations. Elliptic equations, linear and nonlinear, have many relatives: diffusion, ﬂuid mechanics, waves of all types, quantum mechanics, The Laplacian is the King of Differential Operators.

J. L. Vazquez (UAM) Nonlinear Diffusion 4 / Self-organized criticality and convergence to equilibrium of solutions to nonlinear diffusion problems Article in Annual Reviews in Control 34(1) April with 22 Reads.Statistical equilibrium states for the nonlinear Schr??dinger equation Article in Mathematics and Computers in Simulation 55() March with 12 Reads How we measure 'reads'.