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| Author | : Philippe Bénilan |
| Publisher | : |
| Total Pages | : |
| Release | : 1982 |
| Genre | : |
| ISBN | : |
| Author | : Philippe Benilan |
| Publisher | : |
| Total Pages | : 49 |
| Release | : 1982 |
| Genre | : |
| ISBN | : |
This work establishes existence of solutions of the initial-value problem u(t) = delta (determinant u to m-1 power), u(x,0), = u(0)(x), where m> 1, under the most general conditions on u(0). Namely, u(0) need only be such that R to the minus (2 divided by m-1 +N) sum (determinant x or = R) to the power of u(0)(x)) dx is bounded independently of R or = 1. Aronson and Caffarelli have shown this requirement to be necessary. Many auxiliary results are given in the form of estimates on solutions, uniqueness and continuous dependence theorems, etc. While the results may be viewed as 'technical' in that the main points consist of estimates of various sorts, the equation treated is of broad practical interest and the estimates reflect basic properties of the equation. The results obtained are the only ones known to the authors wherein the solvability of a realistic nonlinear initial value problem for a partial differential equation is now understood as completely as in the case of the heat equation.
| Author | : Juan Luis Vazquez |
| Publisher | : Oxford University Press |
| Total Pages | : 624 |
| Release | : 2007 |
| Genre | : Mathematics |
| ISBN | : 9780198569039 |
Aimed at research students and academics in mathematics and engineering, as well as engineering specialists, this book provides a systematic and comprehensive presentation of the mathematical theory of the nonlinear heat equation usually called the Porous Medium Equation.
| Author | : Juan Luis Vazquez |
| Publisher | : Oxford University Press |
| Total Pages | : 647 |
| Release | : 2007 |
| Genre | : Mathematics |
| ISBN | : 0198569033 |
The Heat Equation 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 PDEs, and only recently has it come to be fairly well understood. In this monograph, aimed at research students and academics in mathematics and engineering, as well as engineering specialists, Professor Vazquez provides a systematic and comprehensive presentation of the mathematical theory of the nonlinear heatequation usually called the Porous Medium Equation (PME). This equation appears in a number of physical applications, such as to describe processes involving fluid flow, heat transfer or diffusion. Other applications have been proposed in mathematical biology, lubrication, boundary layer theory, andother fields. Each chapter contains a detailed introduction and is supplied with a section of notes, providing comments, historical notes or recommended reading, and exercises for the reader.
| Author | : W.-M. Ni |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 359 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461396050 |
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.
| Author | : Anvarbek M. Meirmanov |
| Publisher | : Walter de Gruyter |
| Total Pages | : 329 |
| Release | : 2011-07-20 |
| Genre | : Mathematics |
| ISBN | : 311087444X |
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)
| Author | : Enrico Giusti |
| Publisher | : Springer |
| Total Pages | : 295 |
| Release | : 2006-11-14 |
| Genre | : Mathematics |
| ISBN | : 3540397167 |
| Author | : Wolfgang Arendt |
| Publisher | : Birkhäuser |
| Total Pages | : 803 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3034879245 |
Philippe Bénilan was a most original and charismatic mathematician who had a deep and decisive impact on the theory of Nonlinear Evolution Equations. Dedicated to him, Nonlinear Evolution Equations and Related Topics contains research papers written by highly distinguished mathematicians. They are all related to Philippe Benilan's work and reflect the present state of this most active field. The contributions cover a wide range of nonlinear and linear equations.
| Author | : Luigi A. Rosati |
| Publisher | : Springer |
| Total Pages | : 287 |
| Release | : 2006-11-14 |
| Genre | : Mathematics |
| ISBN | : 3540398015 |
| Author | : V. Lakshmikantham |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 618 |
| Release | : 2003 |
| Genre | : Mathematical analysis |
| ISBN | : 9781402017117 |
