Kategoria BISAC: Mathematics >> Differential Equations - General

This book introduces the treatment of linear and nonlinear (quasi-linear) abstract evolution equations by methods from the theory of strongly continuous semigroups. The theoretical part is accessible to graduate students with basic knowledge in functional analysis, with only some examples requiring more specialized knowledge from the spectral theory of linear, self-adjoint operators in Hilbert spaces. Emphasis is placed on equations of the hyperbolic type which are less often treated in the literature.

Many phenomena in social, natural and engineering fields are governed by wave, potential, parabolic heat-conduction, hyperbolic heat-conduction and dual-phase-lagging heat-conduction equations. This monograph examines these equations: their solution structures, methods of finding their solutions under various supplementary conditions, as well as the physical implication and applications of their solutions.

One of the most striking features of Coordination Dynamics is its interdisciplinary character. The problems we are trying to solve in this field range from behavioral phenomena of interlimb coordination and coordination between stimuli and movements (perception-action tasks) through neural activation patterns that can be observed during these tasks to clinical applications and social behavior. It is not surprising that close collaboration among scientists from different fields as psychology, kinesiology, neurology and even physics are imperative to deal with the enormous difficulties we...

This book presents the refereed proceedings of the Seventh International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, held in Ulm, Germany, in August 2006. The proceedings include carefully selected papers on many aspects of Monte Carlo and quasi-Monte Carlo methods and their applications. They also provide information on current research in these very active areas.

In a coherent, exhaustive and progressive way, this book presents the tools for studying local bifurcations of limit cycles in families of planar vector fields. A systematic introduction is given to such methods as division of an analytic family of functions in its ideal of coefficients, and asymptotic expansion of non-differentiable return maps and desingularisation. The exposition moves from classical analytic geometric methods applied to regular limit periodic sets to more recent tools for singular limit sets.

The methods can be applied to theoretical problems such as Hilbert's...

This book contains the proceedings of the International Workshop on Operator Theory and Applications held in Faro, Portugal, September 12 to 15, 2000. It includes 20 selected articles centered on the analysis of various classes of singular operators, the factorization of operator and matrix functions, algebraic methods in approximation theory, and applications in diffraction theory. Some papers are related to topics from fractional calculus, complex analysis, operator algebras, and partial differential equations.

Vsevolod Alekseevich Solonnikov is known as one of the outstanding mathematicians from the St. Petersburg Mathematical School. His remarkable results on exact estimates of solutions to boundary and initial-boundary value problems for linear elliptic, parabolic, Stokes and Navier-Stokes systems, his methods and contributions to the inverstigation of free boundary problems, in particular in fluid mechanics, are well known to specialists all over the world.

The International Conference on "Trends in Partial Differential Equations of Mathematical Physics" was held on the occasion of his...

Award-winning monograph of the Ferran Sunyer i Balaguer Prize 2004.

This book studies regularity properties of Mumford-Shah minimizers. The Mumford-Shah functional was introduced in the 1980s as a tool for automatic image segmentation, but its study gave rise to many interesting questions of analysis and geometric measure theory. The main object under scrutiny is a free boundary K where the minimizer may have jumps. The book presents an extensive description of the known regularity properties of the singular sets K, and the techniques to get them. Some time is spent on the C...

The extraordinary range of cultural interests of renowned physicist David Speiser including the sciences, art, architecture, music, and history of science has inspired generations of later scientists to look beyond the boundaries of their own disciplines. In this book, seventeen scholars from various fields pay tribute to his multifaceted career, addressing topics as varied as music theory and the nuclear arms race.