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| Author | : Chun Wing Sze |
| Publisher | : |
| Total Pages | : 146 |
| Release | : 1992 |
| Genre | : Evolution equations, Nonlinear |
| ISBN | : |
| Author | : Björn E. J. Dahlberg |
| Publisher | : |
| Total Pages | : 36 |
| Release | : 1987 |
| Genre | : |
| ISBN | : |
| Author | : Panagiota Daskalopoulos |
| Publisher | : European Mathematical Society |
| Total Pages | : 216 |
| Release | : 2007 |
| Genre | : Mathematics |
| ISBN | : 9783037190333 |
The book deals with the existence, uniqueness, regularity, and asymptotic behavior of solutions to the initial value problem (Cauchy problem) and the initial-Dirichlet problem for a class of degenerate diffusions modeled on the porous medium type equation $u_t = \Delta u^m$, $m \geq 0$, $u \geq 0$. Such models arise in plasma physics, diffusion through porous media, thin liquid film dynamics, as well as in geometric flows such as the Ricci flow on surfaces and the Yamabe flow. The approach presented to these problems uses local regularity estimates and Harnack type inequalities, which yield compactness for families of solutions. The theory is quite complete in the slow diffusion case ($ m>1$) and in the supercritical fast diffusion case ($m_c
| Author | : American Mathematical Society |
| Publisher | : |
| Total Pages | : 998 |
| Release | : 1993 |
| Genre | : Mathematics |
| ISBN | : |
| Author | : Emmanuele DiBenedetto |
| Publisher | : Springer Nature |
| Total Pages | : 768 |
| Release | : 2023 |
| Genre | : Differential equations, Partial |
| ISBN | : 3031466187 |
This graduate textbook provides a self-contained introduction to the classical theory of partial differential equations (PDEs). Through its careful selection of topics and engaging tone, readers will also learn how PDEs connect to cutting-edge research and the modeling of physical phenomena. The scope of the Third Edition greatly expands on that of the previous editions by including five new chapters covering additional PDE topics relevant for current areas of active research. This includes coverage of linear parabolic equations with measurable coefficients, parabolic DeGiorgi classes, Navier-Stokes equations, and more. The “Problems and Complements” sections have also been updated to feature new exercises, examples, and hints toward solutions, making this a timely resource for students. Partial Differential Equations: Third Edition is ideal for graduate students interested in exploring the theory of PDEs and how they connect to contemporary research. It can also serve as a useful tool for more experienced readers who are looking for a comprehensive reference.
| Author | : B. E. J. Dahlberg |
| Publisher | : |
| Total Pages | : 13 |
| Release | : 1987 |
| Genre | : |
| ISBN | : |
| 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 | : Herbert Amann |
| Publisher | : CRC Press |
| Total Pages | : 212 |
| Release | : 1998-04-01 |
| Genre | : Mathematics |
| ISBN | : 9780582317086 |
The numerous applications of partial differential equations to problems in physics, mechanics, and engineering keep the subject an extremely active and vital area of research. With the number of researchers working in the field, advances-large and small-come frequently. Therefore, it is essential that mathematicians working in partial differential equations and applied mathematics keep abreast of new developments. Progress in Partial Differential Equations, presents some of the latest research in this important field. Both volumes contain the lectures and papers of top international researchers contributed at the Third European Conference on Elliptic and Parabolic Problems. In addition to the general theory of elliptic and parabolic problems, the topics covered at the conference include: applications free boundary problems fluid mechanics general evolution problems ocalculus of variations homogenization modeling numerical analysis The research notes in these volumes offer a valuable update on the state-of-the-art in this important field of mathematics.
| 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 | : John Crank |
| Publisher | : Oxford University Press |
| Total Pages | : 428 |
| Release | : 1979 |
| Genre | : Mathematics |
| ISBN | : 9780198534112 |
Though it incorporates much new material, this new edition preserves the general character of the book in providing a collection of solutions of the equations of diffusion and describing how these solutions may be obtained.
