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Author: Arnd Scheel Publisher: American Mathematical Soc. ISBN: 0821833731 Category : Mathematics Languages : en Pages : 102
Book Description
Includes a paper that studies bifurcations of stationary and time-periodic solutions to reaction-diffusion systems. This title develops a center-manifold and normal form theory for radial dynamics which allows for a complete description of radially symmetric patterns.
Author: Arnd Scheel Publisher: American Mathematical Soc. ISBN: 0821833731 Category : Mathematics Languages : en Pages : 102
Book Description
Includes a paper that studies bifurcations of stationary and time-periodic solutions to reaction-diffusion systems. This title develops a center-manifold and normal form theory for radial dynamics which allows for a complete description of radially symmetric patterns.
Author: Vitaly Volpert Publisher: Springer ISBN: 3034808135 Category : Mathematics Languages : en Pages : 796
Book Description
If we had to formulate in one sentence what this book is about, it might be "How partial differential equations can help to understand heat explosion, tumor growth or evolution of biological species". These and many other applications are described by reaction-diffusion equations. The theory of reaction-diffusion equations appeared in the first half of the last century. In the present time, it is widely used in population dynamics, chemical physics, biomedical modelling. The purpose of this book is to present the mathematical theory of reaction-diffusion equations in the context of their numerous applications. We will go from the general mathematical theory to specific equations and then to their applications. Existence, stability and bifurcations of solutions will be studied for bounded domains and in the case of travelling waves. The classical theory of reaction-diffusion equations and new topics such as nonlocal equations and multi-scale models in biology will be considered.
Author: Markus Kirkilionis Publisher: Springer Science & Business Media ISBN: 3662052814 Category : Mathematics Languages : en Pages : 427
Book Description
Applied mathematics is a central connecting link between scientific observations and their theoretical interpretation. Nonlinear analysis has surely contributed major developments which nowadays shape the face of applied mathematics. At the beginning of the millennium, all sciences are expanding at increased speed. Technological, ecological, economical and medical problem solving is a central issue of every modern society. Mathematical models help to expose fundamental structures hidden in these problems and serve as unifying tools to deepen our understanding. What are the new challenges applied mathematics has to face with the increased diversity of scientific problems? In which direction should the classical tools of nonlinear analysis be developed further? How do new available technologies influence the development of the field? How can problems be solved which have been beyond reach in former times? It is the aim of this book to explore new developments in the field by way of discussion of selected topics from nonlinear analysis.
Author: Nicholas J. Higham Publisher: Princeton University Press ISBN: 0691150397 Category : Mathematics Languages : en Pages : 1014
Book Description
The must-have compendium on applied mathematics This is the most authoritative and accessible single-volume reference book on applied mathematics. Featuring numerous entries by leading experts and organized thematically, it introduces readers to applied mathematics and its uses; explains key concepts; describes important equations, laws, and functions; looks at exciting areas of research; covers modeling and simulation; explores areas of application; and more. Modeled on the popular Princeton Companion to Mathematics, this volume is an indispensable resource for undergraduate and graduate students, researchers, and practitioners in other disciplines seeking a user-friendly reference book on applied mathematics. Features nearly 200 entries organized thematically and written by an international team of distinguished contributors Presents the major ideas and branches of applied mathematics in a clear and accessible way Explains important mathematical concepts, methods, equations, and applications Introduces the language of applied mathematics and the goals of applied mathematical research Gives a wide range of examples of mathematical modeling Covers continuum mechanics, dynamical systems, numerical analysis, discrete and combinatorial mathematics, mathematical physics, and much more Explores the connections between applied mathematics and other disciplines Includes suggestions for further reading, cross-references, and a comprehensive index
Author: Ottmar Loos Publisher: American Mathematical Soc. ISBN: 0821835467 Category : Mathematics Languages : en Pages : 232
Book Description
We develop the basic theory of root systems $R$ in a real vector space $X$ which are defined in analogy to the usual finite root systems, except that finiteness is replaced by local finiteness: the intersection of $R$ with every finite-dimensional subspace of $X$ is finite. The main topics are Weyl groups, parabolic subsets and positive systems, weights, and gradings.
Author: J. T. Cox Publisher: American Mathematical Soc. ISBN: 0821835424 Category : Mathematics Languages : en Pages : 114
Book Description
Studies the evolution of the large finite spatial systems in size-dependent time scales and compare them with the behavior of the infinite systems, which amounts to establishing the so-called finite system scheme. This title introduces the concept of a continuum limit in the hierarchical mean field limit.
Author: Velimir Jurdjevic Publisher: American Mathematical Soc. ISBN: 0821837648 Category : Mathematics Languages : en Pages : 150
Book Description
Studies the elastic problems on simply connected manifolds $M_n$ whose orthonormal frame bundle is a Lie group $G$. This title synthesizes ideas from optimal control theory, adapted to variational problems on the principal bundles of Riemannian spaces, and the symplectic geometry of the Lie algebra $\mathfrak{g}, $ of $G$
Author: Fabio Ancona Publisher: American Mathematical Soc. ISBN: 0821834355 Category : Mathematics Languages : en Pages : 186
Book Description
Considers the Cauchy problem for a strictly hyperbolic $2\times 2$ system of conservation laws in one space dimension $u_t+ F(u)]_x=0, u(0, x)=\bar u(x), $ which is neither linearly degenerate nor genuinely non-linea
Author: Joseph A. Ball Publisher: American Mathematical Soc. ISBN: 0821837680 Category : Mathematics Languages : en Pages : 114
Book Description
The evolution operator for the Lax-Phillips scattering system is an isometric representation of the Cuntz algebra, while the nonnegative time axis for the conservative, linear system is the free semigroup on $d$ letters. This title presents a multivariable setting for Lax-Phillips scattering and for conservative, discrete-time, linear systems.
Author: Arnd Scheel
Author: Arnd Scheel
Author: Vitaly Volpert
Author: Markus Kirkilionis
Author: Nicholas J. Higham
Author: Ottmar Loos
Author: J. T. Cox
Author: K. R. Goodearl
Author: Velimir Jurdjevic
Author: Fabio Ancona
Author: Joseph A. Ball