|
Showing 1 - 6 of
6 matches in All Departments
Although the study of classical thermoelasticity has provided information on linear systems, only recently have results on the asymptotic behavior completed our basic understanding of the generic behavior of solutions. Through systematic work that began in the 80s, we now also understand the basic features of nonlinear systems. Yet some questions remain open, and the field has lacked a comprehensive survey that explores these past results and presents recent developments.
Evolution Equations in Thermoelasticity presents a modern treatment of initial value problems and of initial boundary value problems in both linear and nonlinear thermoelasticity, in one- and multi-dimensional spatial configurations. The authors provide the first self-contained presentation of the subject that offers both introductory parts accessible to graduate students and sophisticated sections valuable to experts.
This book mainly serves as an elementary, self-contained
introduction to several important aspects of the theory of global
solutions to initial value problems for nonlinear evolution
equations. The book employs the classical method of continuation of
local solutions with the help of a priori estimates obtained for
small data. The existence and uniqueness of small, smooth solutions
that are defined for all values of the time parameter are
investigated. Moreover, the asymptotic behaviour of the solutions
is described as time tends to infinity. The methods for nonlinear
wave equations are discussed in detail. Other examples include the
equations of elasticity, heat equations, the equations of
thermoelasticity, Schroedinger equations, Klein-Gordon equations,
Maxwell equations and plate equations. To emphasize the importance
of studying the conditions under which small data problems offer
global solutions, some blow-up results are briefly described.
Moreover, the prospects for corresponding initial boundary value
problems and for open questions are provided. In this second
edition, initial-boundary value problems in waveguides are
additionally considered.
This book mainly serves as an elementary, self-contained
introduction to several important aspects of the theory of global
solutions to initial value problems for nonlinear evolution
equations. The book employs the classical method of continuation of
local solutions with the help of a priori estimates obtained for
small data. The existence and uniqueness of small, smooth solutions
that are defined for all values of the time parameter are
investigated. Moreover, the asymptotic behaviour of the solutions
is described as time tends to infinity. The methods for nonlinear
wave equations are discussed in detail. Other examples include the
equations of elasticity, heat equations, the equations of
thermoelasticity, Schroedinger equations, Klein-Gordon equations,
Maxwell equations and plate equations. To emphasize the importance
of studying the conditions under which small data problems offer
global solutions, some blow-up results are briefly described.
Moreover, the prospects for corresponding initial boundary value
problems and for open questions are provided. In this second
edition, initial-boundary value problems in waveguides are
additionally considered.
This book serves as an elementary, self contained introduction into
some important aspects of the theory of global solutions to initial
value problems for nonlinear evolution equations. The presentation
is made using the classical method of continuation of local
solutions with the help of a priori estimates obtained for small
data.
Das zweibandige Werk umfasst den gesamten Stoff von in der Analysis
ublichen Vorlesungen fur einen sechssemestrigen
Bachelor-Studiengang der Mathematik. Die Bucher sind vorlesungsnah
aufgebaut und bilden die Vorlesungen exakt ab. Jeder Band enthalt
Beispiele und zusatzlich ein Kapitel "Prufungsfragen," das
Studierende auf mundliche und schriftliche Prufungen vorbereiten
soll. Das Werk ist ein Kompendium der Analysis und eignet sich als
Lehr- und Nachschlagewerk sowohl fur Studierende als auch fur
Dozenten.
Das zweibandige Werk umfasst den gesamten Stoff von in der Analysis
ublichen Vorlesungen fur einen sechssemestrigen
Bachelor-Studiengang der Mathematik. Die Bucher sind vorlesungsnah
aufgebaut und bilden die Vorlesungen exakt ab. Jeder Band enthalt
Beispiele und zusatzlich ein Kapitel "Prufungsfragen," das
Studierende auf mundliche und schriftliche Prufungen vorbereiten
soll. Das Werk ist ein Kompendium der Analysis und eignet sich als
Lehr- und Nachschlagewerk sowohl fur Studierende als auch fur
Dozenten.
|
|