Degenerate Differential Equations In Banach Spaces

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Degenerate Differential Equations In Banach Spaces

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Author : Angelo Favini
language : en
Publisher: CRC Press
Release Date : 1998-09-10

Degenerate Differential Equations In Banach Spaces written by Angelo Favini and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-09-10 with Mathematics categories.

This work presents a detailed study of linear abstract degenerate differential equations, using both the semigroups generated by multivalued (linear) operators and extensions of the operational method from Da Prato and Grisvard. The authors describe the recent and original results on PDEs and algebraic-differential equations, and establishes the analyzability of the semigroup generated by some degenerate parabolic operators in spaces of continuous functions.

Differential Equations In Banach Spaces

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Author : Angelo Favini
language : en
Publisher: Springer
Release Date : 2006-12-08

Differential Equations In Banach Spaces written by Angelo Favini and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-08 with Mathematics categories.

Differential Equations In Banach Spaces

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Author : Giovanni Dore
language : en
Publisher: CRC Press
Release Date : 2020-10-07

Differential Equations In Banach Spaces written by Giovanni Dore and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-07 with Mathematics categories.

This reference - based on the Conference on Differential Equations, held in Bologna - provides information on current research in parabolic and hyperbolic differential equations. Presenting methods and results in semigroup theory and their applications to evolution equations, this book focuses on topics including: abstract parabolic and hyperbolic linear differential equations; nonlinear abstract parabolic equations; holomorphic semigroups; and Volterra operator integral equations.;With contributions from international experts, Differential Equations in Banach Spaces is intended for research mathematicians in functional analysis, partial differential equations, operator theory and control theory; and students in these disciplines.

Monotone Operators In Banach Space And Nonlinear Partial Differential Equations

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Author : R. E. Showalter
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-02-22

Monotone Operators In Banach Space And Nonlinear Partial Differential Equations written by R. E. Showalter and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-22 with Mathematics categories.

The objectives of this monograph are to present some topics from the theory of monotone operators and nonlinear semigroup theory which are directly applicable to the existence and uniqueness theory of initial-boundary-value problems for partial differential equations and to construct such operators as realizations of those problems in appropriate function spaces. A highlight of this presentation is the large number and variety of examples introduced to illustrate the connection between the theory of nonlinear operators and partial differential equations. These include primarily semilinear or quasilinear equations of elliptic or of parabolic type, degenerate cases with change of type, related systems and variational inequalities, and spatial boundary conditions of the usual Dirichlet, Neumann, Robin or dynamic type. The discussions of evolution equations include the usual initial-value problems as well as periodic or more general nonlocal constraints, history-value problems, those which may change type due to a possibly vanishing coefficient of the time derivative, and other implicit evolution equations or systems including hysteresis models. The scalar conservation law and semilinear wave equations are briefly mentioned, and hyperbolic systems arising from vibrations of elastic-plastic rods are developed. The origins of a representative sample of such problems are given in the appendix.

Partial Differential Equations And Functional Analysis

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Author : J. Cea
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Partial Differential Equations And Functional Analysis written by J. Cea and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Pierre Grisvard, one of the most distinguished French mathematicians, died on April 22, 1994. A Conference was held in November 1994 out of which grew the invited articles contained in this volume. All of the papers are related to functional analysis applied to partial differential equations, which was Grisvard's specialty. Indeed his knowledge of this area was extremely broad. He began his career as one of the very first students of Jacques Louis Lions, and in 1965, he presented his "State Thesis" on interpolation spaces, using in particular, spectral theory for linear operators in Banach spaces. After 1970, he became a specialist in the study of optimal regularity for par tial differential equations with boundary conditions. He studied singulari ties coming from coefficients, boundary conditions, and mainly non-smooth domains, and left a legacy of precise results which have been published in journals and books. Pierre Grisvard spent most of his career as a full professor at the University of Nice, where he started in 1967. For shorter or longer periods, he visited several foreign countries, and collaborated with some of the most famous mathematicians in his field. He was also an excellent organizer and directed a large number of Ph.D. students. Finally, this volume contains a bibliography of Grisvard's works as well as one paper which he wrote and which has not been published before.

Differential Equations Mathematical Modeling And Computational Algorithms

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Author : Vladimir Vasilyev
language : en
Publisher: Springer Nature
Release Date : 2023-06-06

Differential Equations Mathematical Modeling And Computational Algorithms written by Vladimir Vasilyev and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-06 with Mathematics categories.

This book contains reports made at the International Conference on Differential Equations, Mathematical Modeling and Computational Algorithms, held in Belgorod, Russia, in October 2021 and is devoted to various aspects of the theory of differential equations and their applications in various branches of science. Theoretical papers devoted to the qualitative analysis of emerging mathematical objects, theorems of the existence and uniqueness of solutions to the boundary value problems under study are presented, and numerical algorithms for their solution are described. Some issues of mathematical modeling are also covered; in particular, in problems of economics, computational aspects of the theory of differential equations and boundary value problems are studied. The articles are written by well-known experts and are interesting and useful to a wide audience: mathematicians, representatives of applied sciences and students and postgraduates of universities engaged in applied mathematics.

Linear Sobolev Type Equations And Degenerate Semigroups Of Operators

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Author : Georgy A. Sviridyuk
language : en
Publisher: Walter de Gruyter
Release Date : 2012-06-04

Linear Sobolev Type Equations And Degenerate Semigroups Of Operators written by Georgy A. Sviridyuk and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-04 with Mathematics categories.

Focusing on the mathematics, and providing only a minimum of explicatory comment, this volume contains six chapters covering auxiliary material, relatively p-radial operators, relatively p-sectorial operators, relatively σ-bounded operators, Cauchy problems for inhomogenous Sobolev-type equations, bounded solutions to Sobolev-type equations, and optimal control.

Vector Valued Laplace Transforms And Cauchy Problems

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Author : Wolfgang Arendt
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11

Vector Valued Laplace Transforms And Cauchy Problems written by Wolfgang Arendt and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.

Linear evolution equations in Banach spaces have seen important developments in the last two decades. This is due to the many different applications in the theory of partial differential equations, probability theory, mathematical physics, and other areas, and also to the development of new techniques. One important technique is given by the Laplace transform. It played an important role in the early development of semigroup theory, as can be seen in the pioneering monograph by Rille and Phillips [HP57]. But many new results and concepts have come from Laplace transform techniques in the last 15 years. In contrast to the classical theory, one particular feature of this method is that functions with values in a Banach space have to be considered. The aim of this book is to present the theory of linear evolution equations in a systematic way by using the methods of vector-valued Laplace transforms. It is simple to describe the basic idea relating these two subjects. Let A be a closed linear operator on a Banach space X. The Cauchy problern defined by A is the initial value problern (t 2 0), (CP) {u'(t) = Au(t) u(O) = x, where x E X is a given initial value. If u is an exponentially bounded, continuous function, then we may consider the Laplace transform 00 u(>. ) = 1 e-). . tu(t) dt of u for large real>. .

Differential Equations And Control Theory

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Author : Sergiu Aizicovici
language : en
Publisher: CRC Press
Release Date : 2001-10-02

Differential Equations And Control Theory written by Sergiu Aizicovici and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-10-02 with Mathematics categories.

Provides comprehensive coverage of the most recent developments in the theory of non-Archimedean pseudo-differential equations and its application to stochastics and mathematical physics--offering current methods of construction for stochastic processes in the field of p-adic numbers and related structures. Develops a new theory for parabolic equations over non-Archimedean fields in relation to Markov processes.

Differential Equations

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Author : Angelo Favini
language : en
Publisher: CRC Press
Release Date : 2006-06-09

Differential Equations written by Angelo Favini and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-09 with Mathematics categories.

With contributions from some of the leading authorities in the field, the work in Differential Equations: Inverse and Direct Problems stimulates the preparation of new research results and offers exciting possibilities not only in the future of mathematics but also in physics, engineering, superconductivity in special materials, and other scientifi