In this book we present a significant part ofthe material given in an autumn school on "Nonlinear Analysis and Differential Equations," held at the CMAF (Centro de Matematica e Aplica
In this book we present a significant part ofthe material given in an autumn school on "Nonlinear Analysis and Differential Equations," held at the CM...
This book examines a system of parabolic-elliptic partial differential eq- tions proposed in mathematical biology, statistical mechanics, and chemical kinetics. In the context of biology, this system of equations describes the chemotactic feature of cellular slime molds and also the capillary formation of blood vessels in angiogenesis. There are several methods to derive this system. One is the biased random walk of the individual, and another is the reinforced random walk of one particle modelled on the cellular automaton. In the context of statistical mechanics or chemical kinetics, this...
This book examines a system of parabolic-elliptic partial differential eq- tions proposed in mathematical biology, statistical mechanics, and chemical...
In modern theoretical physics, gauge field theories are of great importance since they keep internal symmetries and account for phenomena such as spontaneous symmetry breaking, the quantum Hall effect, charge fractionalization, superconductivity and supergravity. This monograph discusses specific examples of selfdual gauge field structures, including the Chern Simons model, the abelian Higgs model, and Yang Mills gauge field theory.
The author builds a foundation for gauge theory and selfdual vortices by introducing the basic mathematical language of gauge theory and formulating...
In modern theoretical physics, gauge field theories are of great importance since they keep internal symmetries and account for phenomena such as s...
Semiconcavity is a natural generalization of concavity that retains most of the good properties known in convex analysis, but arises in a wider range of applications. This text is the first comprehensive exposition of the theory of semiconcave functions, and of the role they play in optimal control and Hamilton-Jacobi equations.
The first part covers the general theory, encompassing all key results and illustrating them with significant examples. The latter part is devoted to applications concerning the Bolza problem in the calculus of variations and optimal exit time problems for...
Semiconcavity is a natural generalization of concavity that retains most of the good properties known in convex analysis, but arises in a wider ran...
This four-part text beautifully interweaves theory and applications in Fuchsian Reduction. Background results in weighted Sobolev and Holder spaces as well as Nash-Moser implicit function theorem are provided. Most chapters contain a problem section and notes with references to the literature. This volume can be used as a text in graduate courses in PDEs and/or Algebra, or as a resource for researchers working with applications to Fuchsian Reduction. The comprehensive approach features the inclusion of problems and bibliographic notes.
This four-part text beautifully interweaves theory and applications in Fuchsian Reduction. Background results in weighted Sobolev and Holder spaces...
This paper is concerned with the existence and uniform decay rates of solutions of the waveequation with a sourceterm and subject to nonlinear boundary damping ? ? u u =-u- u in ? x(0, +?) ? tt ? ? ? ? u=0 on ? x(0, +?) 0 (1. 1) ? ? u+g(u)=0 on ? x(0, +?) ? t 1 ? ? ? ? 0 1 u(x,0) = u (x); u (x,0) = u (x), x? ?, t n where ? is a bounded domain of R, n? 1, with a smooth boundary ? = ? . 0 1 Here, ? and ? are closed and disjoint and ? represents the unit outward normal 0 1 to ?. Problems like (1. 1), more precisely, ? u u =?f (u)in? x(0, +?) ? tt 0 ? ? ? ? u=0 on ? x(0, +?) 0 (1. 2) ? ? u =?g(u...
This paper is concerned with the existence and uniform decay rates of solutions of the waveequation with a sourceterm and subject to nonlinear boundar...
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...
Vsevolod Alekseevich Solonnikov is known as one of the outstanding mathematicians from the St. Petersburg Mathematical School. His remarkable resul...
This volume contains the proceedings of the international workshop Variational Problems in Materials Science. Coverage includes the study of BV vector fields, path functionals over Wasserstein spaces, variational approaches to quasi-static evolution, free-discontinuity problems with applications to fracture and plasticity, systems with hysteresis or with interfacial energies, evolution of interfaces, multi-scale analysis in ferromagnetism and ferroelectricity, and much more.
This volume contains the proceedings of the international workshop Variational Problems in Materials Science. Coverage includes the study of BV vec...
Maximum principles are bedrock results in the theory of second order elliptic equations. This principle, simple enough in essence, lends itself to a quite remarkable number of subtle uses when combined appropriately with other notions. Intended for a wide audience, the book provides a clear and comprehensive explanation of the various maximum principles available in elliptic theory, from their beginning for linear equations to recent work on nonlinear and singular equations.
Maximum principles are bedrock results in the theory of second order elliptic equations. This principle, simple enough in essence, lends itself to ...
The fascinating ?eld of shape optimization problems has received a lot of attention in recent years, particularly in relation to a number of applications in physics and engineering that require a focus on shapes instead of parameters or functions. The goal of these applications is to deform and modify the admissible shapes in order to comply with a given cost function that needs to be optimized. In this respect the problems are both classical (as the isoperimetric problem and the Newton problem of the ideal aerodynamical shape show) and modern (re?ecting the many results obtained in the last...
The fascinating ?eld of shape optimization problems has received a lot of attention in recent years, particularly in relation to a number of applicati...
