The Cauchy Problem For Higher Order Abstract Differential Equations
Download The Cauchy Problem For Higher Order Abstract Differential Equations full books in PDF, epub, and Kindle. Read online free The Cauchy Problem For Higher Order Abstract Differential Equations ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
The Cauchy Problem for Higher Order Abstract Differential Equations
Author | : Ti-Jun Xiao,Jin Liang |
Publsiher | : Springer |
Total Pages | : 314 |
Release | : 2013-12-11 |
Genre | : Mathematics |
ISBN | : 9783540494799 |
Download The Cauchy Problem for Higher Order Abstract Differential Equations Book in PDF, Epub and Kindle
The main purpose of this book is to present the basic theory and some recent de velopments concerning the Cauchy problem for higher order abstract differential equations u(n)(t) + ~ AiU(i)(t) = 0, t ~ 0, { U(k)(O) = Uk, 0 ~ k ~ n-l. where AQ, Ab . . . , A - are linear operators in a topological vector space E. n 1 Many problems in nature can be modeled as (ACP ). For example, many n initial value or initial-boundary value problems for partial differential equations, stemmed from mechanics, physics, engineering, control theory, etc. , can be trans lated into this form by regarding the partial differential operators in the space variables as operators Ai (0 ~ i ~ n - 1) in some function space E and letting the boundary conditions (if any) be absorbed into the definition of the space E or of the domain of Ai (this idea of treating initial value or initial-boundary value problems was discovered independently by E. Hille and K. Yosida in the forties). The theory of (ACP ) is closely connected with many other branches of n mathematics. Therefore, the study of (ACPn) is important for both theoretical investigations and practical applications. Over the past half a century, (ACP ) has been studied extensively.
The Cauchy Problem for Higher Order Abstract Differential Equations
Author | : Ti-Jun Xiao,Jin Liang |
Publsiher | : Unknown |
Total Pages | : 324 |
Release | : 2014-09-01 |
Genre | : Electronic Book |
ISBN | : 3662178605 |
Download The Cauchy Problem for Higher Order Abstract Differential Equations Book in PDF, Epub and Kindle
Abstract Cauchy Problems
Author | : Irina V. Melnikova,Alexei Filinkov |
Publsiher | : CRC Press |
Total Pages | : 259 |
Release | : 2001-03-27 |
Genre | : Mathematics |
ISBN | : 9781420035490 |
Download Abstract Cauchy Problems Book in PDF, Epub and Kindle
Although the theory of well-posed Cauchy problems is reasonably understood, ill-posed problems-involved in a numerous mathematical models in physics, engineering, and finance- can be approached in a variety of ways. Historically, there have been three major strategies for dealing with such problems: semigroup, abstract distribution, and regularizat
Theory and Applications of Abstract Semilinear Cauchy Problems
Author | : Pierre Magal,Shigui Ruan |
Publsiher | : Springer |
Total Pages | : 543 |
Release | : 2018-11-21 |
Genre | : Mathematics |
ISBN | : 9783030015060 |
Download Theory and Applications of Abstract Semilinear Cauchy Problems Book in PDF, Epub and Kindle
Several types of differential equations, such as functional differential equation, age-structured models, transport equations, reaction-diffusion equations, and partial differential equations with delay, can be formulated as abstract Cauchy problems with non-dense domain. This monograph provides a self-contained and comprehensive presentation of the fundamental theory of non-densely defined semilinear Cauchy problems and their applications. Starting from the classical Hille-Yosida theorem, semigroup method, and spectral theory, this monograph introduces the abstract Cauchy problems with non-dense domain, integrated semigroups, the existence of integrated solutions, positivity of solutions, Lipschitz perturbation, differentiability of solutions with respect to the state variable, and time differentiability of solutions. Combining the functional analysis method and bifurcation approach in dynamical systems, then the nonlinear dynamics such as the stability of equilibria, center manifold theory, Hopf bifurcation, and normal form theory are established for abstract Cauchy problems with non-dense domain. Finally applications to functional differential equations, age-structured models, and parabolic equations are presented. This monograph will be very valuable for graduate students and researchers in the fields of abstract Cauchy problems, infinite dimensional dynamical systems, and their applications in biological, chemical, medical, and physical problems.
Abstract Differential Equations
Author | : Samuel Zaidman |
Publsiher | : San Francisco : Pitman Advanced Pub. Program |
Total Pages | : 156 |
Release | : 1979 |
Genre | : Cauchy problem |
ISBN | : UCAL:B4405910 |
Download Abstract Differential Equations Book in PDF, Epub and Kindle
This monograph deals with linear differential equations in Banach and Hilbert spaces whose coefficients are linear unbounded operators. Looking for examples or applications, the most natural ones are found in the theory of partial differential equations: if to one of the variables is given a privilegiate position and all the others are put together obtains 'at once' an ordinary 'differential' equation with respect to the variable. Adding boundary conditions in order to ensure definiteness of the solutions can often be translated in terms of considering solutions in some convenient linear--often normed--function spaces.
Some Aspects of Cauchy s Problem
Author | : Elinar Hille |
Publsiher | : Unknown |
Total Pages | : 20 |
Release | : 1954 |
Genre | : Cauchy problem |
ISBN | : UOM:39015095242494 |
Download Some Aspects of Cauchy s Problem Book in PDF, Epub and Kindle
The Cauchy Problem
Author | : Hector O. Fattorini |
Publsiher | : Cambridge University Press |
Total Pages | : 664 |
Release | : 1983 |
Genre | : Mathematics |
ISBN | : 9780521302388 |
Download The Cauchy Problem Book in PDF, Epub and Kindle
This volume deals with the Cauchy or initial value problem for linear differential equations. It treats in detail some of the applications of linear space methods to partial differential equations, especially the equations of mathematical physics such as the Maxwell, Schrödinger and Dirac equations. Background material presented in the first chapter makes the book accessible to mathematicians and physicists who are not specialists in this area as well as to graduate students.
Lectures on Cauchy s Problem in Linear Partial Differential Equations
Author | : Jacques Hadamard |
Publsiher | : Courier Corporation |
Total Pages | : 328 |
Release | : 2003-01-01 |
Genre | : Mathematics |
ISBN | : 0486495493 |
Download Lectures on Cauchy s Problem in Linear Partial Differential Equations Book in PDF, Epub and Kindle
Basing his research on prior studies by Riemann, Kirchhoff, and Volterra, the author extends and improves Volterra's work, applying its theories relating to spherical and cylindrical waves to all normal hyperbolic equations. 1923 edition.