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Thursday, April 30, 2020 | History

1 edition of Degenerate Nonlinear Diffusion Equations found in the catalog.

Degenerate Nonlinear Diffusion Equations

Written in English

Subjects:
• Mathematics,
• Mathematical optimization,
• Calculus of Variations and Optimal Control; Optimization,
• Partial Differential equations,
• Applications of Mathematics

• Edition Notes

The Physical Object ID Numbers Statement by Angelo Favini, Gabriela Marinoschi Series Lecture Notes in Mathematics -- 2049 Contributions Marinoschi, Gabriela, SpringerLink (Online service) Format [electronic resource] / Open Library OL27029941M ISBN 10 9783642282850

We have presented a study on the effect of the incorporation of a nonlinear advection term in the degenerate reaction-diffusion equation. When investigating the traveling wave behavior, we found that the “advection speed” influences the type and the speed of the possible traveling maisondesvautours.com: Faustino Sánchez-Garduño, Judith Pérez-Velázquez. We prove the existence of non-trivial global minimizers of a class of free energies related to aggregation equations with degenerate diffusion on $\\Real^d$.

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The problems concern nonlinear parabolic equations involving two cases of degeneracy. More precisely, one case Degenerate Nonlinear Diffusion Equations book due to the vanishing of the time derivative coefficient and the other is provided by the vanishing of the diffusion coefficient on subsets of positive measure of the domain.

However, this work does not seek to present an exhaustive study of degenerate diffusion equations, Degenerate Nonlinear Diffusion Equations book rather to emphasize some rigorous and efficient techniques for approaching various problems involving degenerate nonlinear diffusion equations, such as well-posedness, periodic solutions, asymptotic behaviour, discretization schemes, coefficient identification, and to introduce Degenerate Nonlinear Diffusion Equations book solving.

Concentrating on a class of equations with nonlinearities of power type that lead to degenerate or singular parabolicity ("equations of Degenerate Nonlinear Diffusion Equations book medium type"), the aim of this text is to obtain sharp a priori estimates and decay rates for general classes of solutions in terms of estimates of particular maisondesvautours.com: Juan Luis Vázquez.

In this chapter we present another method Degenerate Nonlinear Diffusion Equations book studying the well-posedness of a multivalued degenerate fast diffusion equation by proposing an appropriate time discretization scheme.

Degenerate Nonlinear Diffusion Equations book Nov 01,  · 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; Cahn–Hilliard Equation with Constant Mobility.

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.

This book provides a new focus on the increasing use of mathematical applications in the life sciences, while also addressing key topics such as linear PDEs, first-order nonlinear PDEs, classical and weak solutions, shocks, hyperbolic systems, nonlinear diffusion, and elliptic equations.

The Night Fire. Michael Connelly. € €. Lecture Non-linear Diﬀusion Scribe: Lou Odette - American International Group (AIG) October 17, 1 Non-linear Drift In the continuum limit the PDF ρ(x,t) for the position x at time t of a single random walker satisﬁes the Fokker-Plank equation (FPE), based on.

May 08,  · The problems concern nonlinear parabolic equations involving two cases of degeneracy. More precisely, one case is due to the vanishing of the time derivative coefficient and the other is provided by the vanishing of the diffusion coefficient Brand: Springer Berlin Heidelberg.

Get this from a library. Degenerate nonlinear diffusion equations. [A Favini; Gabriela Marinoschi] -- "The aim of these notes is to include in a uniform presentation style several Degenerate Nonlinear Diffusion Equations book related to the theory of degenerate nonlinear diffusion equations, treated in the mathematical framework of.

Degenerate Nonlinear Diffusion Equations. Summary: The aim of these notes is to include in a uniform presentation style several topics related to the theory of degenerate nonlinear diffusion equations, treated in the mathematical framework of evolution equations with multivalued m-accretive operators in.

Outline 1 Theories of Diffusion Diffusion Heat equation Linear Parabolic Equations Nonlinear equations 2 Degenerate Diffusion and Free Boundaries Introduction Degenerate Nonlinear Diffusion Equations book basics Generalities 3 Fast Diffusion Equation Fast Diffusion Ranges J.

Vazquez (UAM) Nonlinear Diffusion 2 / This book provides a presentation of the mathematical theory of the nonlinear heat equation usually called the Porous Medium Equation (PME). This equation appears in a number of physical Author: Yunguang Lu.

The second part is novel compared to the PME, for which the planar wave is exactly linear. p= cxat in nity. Once again, we prove this statement for the nal viscosity solution, but.

the proof extends to the -solutions. Section 6 is nally devoted to uniqueness of the wave. pro les, and we establish. Theorem Cited by: 1. Traveling wave solutions are discussed for nonlinear diffusion equations where the nonlinearity occurs in the diffusion flux as well as in a source term.

For a variety of nonlinear diffusion fluxes it is shown that wave solutions exist if and only if the wave speed is greater than some critical maisondesvautours.com by: Nonlinear diffusion, degenerate parabolic equations, ﬂows in porous media.

Introduction The heat equation, ∂tu = u, (HE for short) is one of the three classical linear partial differential equations of second order that form the basis of any elementary introduction to the area of partial differential equations.

Its success in describing. 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. This paper is concerned with a system of quasilinear reaction–diffusion equations with density dependent diffusion coefficients and mixed quasimonotone reaction functions.

The equations are allowed to be degenerate and the boundary conditions are of the nonlinear type. () Uniqueness and existence for anisotropic degenerate parabolic equations with boundary conditions on a bounded rectangle.

Journal of Differential Equations() Degenerate triply nonlinear problems with nonhomogeneous boundary conditions. Central European Journal of MathematicsCited by: Journal of Differential Equations1 21 () On Solutions to Nonlinear Reaction Diffusion Convection Equations with Degenerate Diffusion Yunguang Lu Departamento de Matema ticas y [email protected] stica, Universidad Nacional de Colombia, Bogota, Colombia E-mail: yglu maisondesvautours.com and Willi Ja˘ ger.

Nov 26,  · This paper presents a full classification of the short-time behavior of the interfaces in the Cauchy problem for the nonlinear second order degenerate parabolic PDEAuthor: Ugur G.

Abdulla, Amna Abuweden. Nonlinear and Nonlocal Degenerate Diffusions on Bounded Domains Matteo Bonforte Departamento de Matemáticas, A Priori Estimates for Fractional Nonlinear Degenerate Diffusion Equations on bounded domains.

Arch. Rat. Mech. Anal. [BV2]M. B., J. VÁZQUEZ, Fractional Nonlinear Degenerate Diffusion Equations on Bounded Domains Part I. Haraux, P. PoláčikConvergence to a positive equilibrium for some nonlinear evolution equations in a ball Acta Math.

Univ. Comeniane, 61 (), pp. Google ScholarCited by: This book deals with the long-time behavior of solutions of degenerate parabolic dissipative equations arising in the study of biological, ecological, and physical problems.

Examples include porous media equations, $$p$$-Laplacian and doubly nonlinear equations, as well as degenerate diffusion equations with chemotaxis and ODE-PDE coupling systems. Nov 01,  · The aim of this paper is to investigate the asymptotic behaviour as t → ∞ of the solutions to the Cauchy problem for the nonlinear degenerate KPP-type diffusion-reaction equation u t = (u m) xx + u p - u q, where m,p and q are positive parameters.

Our result is similar to the corresponding one of Kolmogorov, Petrowsky and Piscunov; namely Cited by: We study a reaction diffusion model recently proposed in [5] to describe the spatiotemporal evolution of the bacterium Bacillus subtilis on agar plates containing nutrient.

An interesting mathematical feature of the model, which is a coupled pair of partial differential equations, is that the bacterial density satisfies a degenerate nonlinear diffusion maisondesvautours.com by: We investigate the diffusion-aggregation equations with degenerate diffusion $\Delta u^m$ and singular interaction kernel $\mathcal{K}_s = (-\Delta)^{-s}$ with $s\in(0,\frac{d}{2})$.

The equation is related to biological aggregation models. We analyze the regime where the diffusive force is stronger than the aggregation maisondesvautours.com: Yuming Paul Zhang. Buy Travelling Waves in Nonlinear Diffusion-Convection Reaction (Progress in Nonlinear Differential Equations and Their Applications) on maisondesvautours.com FREE SHIPPING on qualified ordersCited by: sion coefficient u is zero when u = 0; this is sometimes referred to as "degenerate diffusion." S~nchez-Gardufio and Maini [17] showed that for a large family of reaction-diffusion equations with degenerate nonlinear diffusion, including (2), there is a travelling wave of sharp-front type.

ON A NONLINEAR DEGENERATE PARABOLIC TRANSPORT-DIFFUSION EQUATION WITH A DISCONTINUOUS COEFFICIENT KENNETH H. KARLSEN, NILS H. RISEBRO, & JOHN D. TOWERS Abstract. We study the Cauchy problem for the nonlinear (possibly strongly) degenerate parabolic transport-di usion equation.

Page - Evolution of a stable profile for a class of nonlinear diffusion equations with fixed boundaries, J. ‎ Appears in 21 books from Page - DiBenedetto and MA Herrero, On the Cauchy problem and initial traces for a degenerate parabolic equation, Trans.

Amer. Math. Soc. This monograph has grown out of research we started inalthough the foun­ dations were laid in the '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. Reaction–diffusion systems are mathematical models which correspond to several physical phenomena. The most common is the change in space and time of the concentration of one or more chemical substances: local chemical reactions in which the substances are transformed into each other, and diffusion which causes the substances to spread out over a surface in space.

Buy Travelling Waves in Nonlinear Diffusion-Convection Reaction (Progress in Nonlinear Differential Equations and Their Applications) by Brian H. Gilding, Robert Kersner (ISBN: ) from Amazon's Book Store. Everyday low prices and free delivery on eligible orders. Quick Search in Books. Enter words / phrases / DOI / ISBN / keywords / authors / etc Cahn-Hilliard Equation with Degenerate Mobility.

Models with degenerate mobility. Nonlinear Diffusion Equations. Non-Newtonian Filtration Equations. Nonlinear Diffusion Equations. Newtonian Filtration Equations. Nonlinear Diffusion Equations.

Nonlinear. In this paper we discuss a high order WENO finite difference discretization for nonlinear degenerate parabolic equations which may contain discontinuous solutions.

A porous medium equation (PME) is used as an example to demonstrate the algorithm structure and maisondesvautours.com by: PUBLICATIONS Books Carroll, Robert Wayne; Showalter, Ralph E. SINGULAR and DEGENERATE CAUCHY PROBLEMS. Mathematics in Science and Engineering, Vol.

Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, viii+ pp. Smoothing and Decay Estimates for Nonlinear Diffusion Equations: Equations of Porous Medium Type (Oxford Lecture Series in Mathematics and Its Applications Book 33) eBook: Juan Luis Vázquez: maisondesvautours.com: Kindle StoreAuthor: Juan Luis Vázquez.

in a Reaction-Diffusion Equation with Degenerate Nonlinear Diffusion J.A. Sherratt ¤ Department of Mathematics and Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK Abstract.

Reaction-diffusion equations with degenerate nonlinear diffusion are in widespread use as models of biological maisondesvautours.com by:. Numerical Treatment pdf Degenerate Diffusion Equations via Feller’s Boundary Classiﬁcation, and Applications Emanuela Cacio,1 Stephen E.

Cohn,2 Renato Spigler1 1Dipartimento di Matematica, Università “Roma Tre”, 1, Largo S.L. Murialdo, Rome, Italy.University of Cergy-Pontoise, Cergy Pontoise, France Expertise: NonLinear Pde's, One Laplacian, Viscosity solutions for singular or degenerate Fully Nonlinear equations, Regularity S.

Dragomir University of Basilicata, Potenza, Italy Expertise: Nonlinear PDEs of variational origin on CR and Lorentzian manifolds, (subelliptic) harmonic maps.Topol. Methods Nonlinear Ebook.

Volume 35, Number 1 (), Traveling front solutions in nonlinear diffusion degenerate Fisher-KPP and Nagumo equations via the Conley indexCited by: 2.