This book presents new accurate and efficient exponentially convergent methods for abstract differential equations with unbounded operator coefficients in Banach space. These methods are highly relevant forpractical scientific computing since the equations under consideration can be seen as the meta-models of systems of ordinary differential equations (ODE) as well as of partial differential equations (PDEs) describing various applied problems. The framework of functional analysis allows one to obtain very general but at the same time transparent algorithms and mathematical results which...
This book presents new accurate and efficient exponentially convergent methods for abstract differential equations with unbounded operator coeffici...
Until the mid-twentieth century, topological studies were focused on the theory of suitable structures on sets of points. The concept of open set exploited since the twenties offered an expression of the geometric intuition of a "realistic" place (spot, grain) of non-trivial extent.
Imitating the behaviour of open sets and their relations led to a new approach to topology flourishing since the end of the fifties.It has proved to be beneficial in many respects. Neglecting points, only little information was lost, while deeper insights have been gained; moreover, many results...
Until the mid-twentieth century, topological studies were focused on the theory of suitable structures on sets of points. The concept of open set e...
This book contains an exposition of several results related with direct and converse theorems in the theory of approximation by algebraic polynomials in a finite interval. In addition, some facts concerning trigonometric approximation that are necessary for motivation and comparisons are included. The selection of papers that are referenced and discussed document some trends in polynomial approximation from the 1950s to the present day.
This book contains an exposition of several results related with direct and converse theorems in the theory of approximation by algebraic polynomials ...
Including previously unpublished material, this volume presents recent results on nonlinear parabolic-hyperbolic coupled systems such as the compressible Navier-Stokes equations. It also summarizes the latest research by the authors and their collaborators.
Including previously unpublished material, this volume presents recent results on nonlinear parabolic-hyperbolic coupled systems such as the compressi...
This book focuses on the interplay between Eulerian and Lagrangian conservation laws for systems that admit physical motivation and originate from continuum mechanics.
This book focuses on the interplay between Eulerian and Lagrangian conservation laws for systems that admit physical motivation and originate from con...
An asymmetric norm is a positive definite sublinear functional p on a real vector space X. The topology generated by the asymmetric norm p is translation invariant so that the addition is continuous, but the asymmetry of the norm implies that the multiplication by scalars is continuous only when restricted to non-negative entries in the first argument. The asymmetric dual of X, meaning the set of all real-valued upper semi-continuous linear functionals on X, is merely a convex cone in the vector space of all linear functionals on X. In spite of these...
An asymmetric norm is a positive definite sublinear functional p on a real vector space X. The topology generated by the asymmetric norm...
Harmonic maps between Riemannian manifolds were first established by James Eells and Joseph H. Sampson in 1964. Wave maps are harmonic maps on Minkowski spaces and have been studied since the 1990s. Yang-Mills fields, the critical points of Yang-Mills functionals of connections whose curvature tensors are harmonic, were explored by a few physicists in the 1950s, and biharmonic maps (generalizing harmonic maps) were introduced by Guoying Jiang in 1986. The book presents an overview of the important developments made in these fields since they first came up. Furthermore, it introduces biwave...
Harmonic maps between Riemannian manifolds were first established by James Eells and Joseph H. Sampson in 1964. Wave maps are harmonic maps on Minkows...
Differential equations with delay naturallyarise in various applications, such as control systems, viscoelasticity, mechanics, nuclear reactors, distributed networks, heat flows, neural networks, combustion, interaction of species, microbiology, learning models, epidemiology, physiology, and many others. This book systematically investigates the stability of linear as well as nonlinear vector differential equations with delay and equations with causal mappings. It presents explicit conditions for exponential, absolute and input-to-state stabilities. These stability conditions are mainly...
Differential equations with delay naturallyarise in various applications, such as control systems, viscoelasticity, mechanics, nuclear reactors, di...
This book presents recent results on nonlinear evolutionary fluid equations such as the compressible (radiative) magnetohydrodynamics (MHD) equations, compressible viscous micropolar fluid equations, the full non-Newtonian fluid equations and non-autonomous compressible Navier-Stokes equations. These types of partial differential equations arise in many fields of mathematics, but also in other branches of science such as physics and fluid dynamics.
This book will be a valuable resource for graduate students and researchers interested in partial differential equations, and will also...
This book presents recent results on nonlinear evolutionary fluid equations such as the compressible (radiative) magnetohydrodynamics (MHD) equatio...
The purpose of this book is to develop the foundations of the theory of holomorphicity on the ring of bicomplex numbers. Accordingly, the main focus is on expressing the similarities with, and differences from, the classical theory of one complex variable. The result is an elementary yet comprehensive introduction to the algebra, geometry and analysis of bicomplex numbers.
Around the middle of the nineteenth century, several mathematicians (the best known being Sir William Hamilton and Arthur Cayley) became interested in studying number systems that extended the field...
The purpose of this book is to develop the foundations of the theory of holomorphicity on the ring of bicomplex numbers. Accordingly,...
