The lecture courses of the CIME Summer School on Probabilistic Models for Nonlinear PDE's and their Numerical Applications (April 1995) had a three-fold emphasis: first, on the weak convergence of stochastic integrals; second, on the probabilistic interpretation and the particle approximation of equations coming from Physics (conservation laws, Boltzmann-like and Navier-Stokes equations); third, on the modelling of networks by interacting particle systems.
These lecture notes are woven around the subject of Burgers' turbulence/KPZ model of interface growth, a study of the nonlinear parabolic equation with random initial data.
Most books devoted to the theory of the integral have ignored the nonabsolute integrals, despite the fact that the journal literature relating to these has become richer and richer.
Using harmonic maps, non-linear PDE and techniques from algebraic geometry this book enables the reader to study the relation between fundamental groups and algebraic geometry invariants of algebraic varieties.
While optimality conditions for optimal control problems with state constraints have been extensively investigated in the literature the results pertaining to numerical methods are relatively scarce.
This book starts with an overview of the research of Grobner bases which have many applications in various areas of mathematics since they are a general tool for the investigation of polynomial systems.
When the DFG (Deutsche Forschungsgemeinschaft) launched its collabora- tive research centre or SFB (Sonderforschungsbereich) 438 "e;Mathematical Modelling, Simulation, and Verification in Material-Oriented Processes and Intelligent Systems"e; in July 1997 at the Technische Vniversitat Munchen and at the Vniversitat Augsburg, southern Bavaria got its second nucleus of the still young discipline scientific computing.
This book, suitable for graduate students and professional mathematicians alike, didactically introduces methodologies due to Furstenberg and others for attacking problems in chromatic and density Ramsey theory via recurrence in topological dynamics and ergodic theory, respectively.
Domain decomposition methods provide powerful and flexible tools for the numerical approximation of partial differential equations arising in the modeling of many interesting applications in science and engineering.
Measure and integration wereonceconsidered,especially by many ofthe more practically inclined, to be an esoteric area ofabstract mathematics best left to pure mathematicians.
The main objective of this monograph is the study of a class of stochastic differential systems having unbounded coefficients, both in finite and in infinite dimension.
This book contains a detailed exposition of Carleson-Hunt theorem following the proof of Carleson: to this day this is the only one giving better bounds.
The notion of amenability has its origins in the beginnings of modern measure theory: Does a finitely additive set function exist which is invariant under a certain group action?
Moment Theory is not a new subject; however, in classical treatments, the ill-posedness of the problem is not taken into account - hence this monograph.
Operator Functions and Localization of Spectra is the first book that presents a systematic exposition of bounds for the spectra of various linear nonself-adjoint operators in a Hilbert space, having discrete and continuous spectra.
Optimal Shape Design is concerned with the optimization of some performance criterion dependent (besides the constraints of the problem) on the "e;shape"e; of some region.
The monograph is concerned with the modulus of families of curves on Riemann surfaces and its applications to extremal problems for conformal, quasiconformal mappings, and the extension of the modulus onto Teichmuller spaces.
This volume of original research papers from the Israeli GAFA seminar during the years 1996-2000 not only reports on more traditional directions of Geometric Functional Analysis, but also reflects on some of the recent new trends in Banach Space Theory and related topics.
