Kategoria BISAC: Mathematics >> Differential Equations - General

In this text the authors consider the Korteweg-de Vries (KdV) equation (u_t = - u_xxx + 6uu_x) with periodic boundary conditions. Derived to describe long surface waves in a narrow and shallow channel, this equation in fact models waves in homogeneous, weakly nonlinear and weakly dispersive media in general.

Viewing the KdV equation as an infinite dimensional, and in fact integrable Hamiltonian system, we first construct action-angle coordinates which turn out to be globally defined. They make evident that all solutions of the periodic KdV equation are...

Sobolev spaces and inequalities are fundamental tools in the theory of partial differential equations, analysis, differential geometry, mathematical physics, etc. Introduced 70 years ago, they turned out to be extremely useful in many different settings and continue to attract the attention of new generations of mathematicians. Recent advantages in the theory of Sobolev spaces and in applications are presented by globally recognized specialists in topics covering Sobolev-type spaces of functions in metric spaces, various aspects of Sobolev-type inequalities, boundary value problems for...

Cardiovascular diseases have a major impact in Western countries. Mathematical models and numerical simulations can aid the understanding of physiological and pathological processes, complementing the information provided to medical doctors by medical imaging and other non-invasive means, and opening the possibility of a better diagnosis and more in-depth surgical planning.This book offers a mathematically sound and up-to-date foundation to the training of researchers, and serves as a useful reference for the development of mathematical models and numerical simulation codes. It is...

This book presents several recent developments in the theory of hyperbolic equations. The carefully selected invited and peer-reviewed contributions deal with questions of low regularity, critical growth, ill-posedness, decay estimates for solutions of different non-linear hyperbolic models, and introduce new approaches based on microlocal methods.

Capturing the state of the art of the interplay between partial differential equations, functional analysis, maximal regularity, and probability theory, this volume was initiated at the Delft conference on the occasion of the retirement of Philippe Clement. It will be of interest to researchers in PDEs and functional analysis.

Decomposable sets since T. R. Rockafellar in 1968 are one of basic notions in nonlinear analysis, especially in the theory of multifunctions. A subset K of measurable functions is called decomposable if

(Q) for all and measurable A.

This book attempts to show the present stage of "decomposable analysis" from the point of view of fixed point theory. The book is split into three parts, beginning with the background of functional analysis, proceeding to the theory of multifunctions and lastly, the decomposability property.

Mathematicians and students...