Differential Inclusions: Set-Valued Maps and Viability Theory Grundlehren der mathematischen Wissenschaften 264

Aubin, J.-P. and A. Cellina:

ISBN 10: 3540131051 / ISBN 13: 9783540131052

Published by Springer Verlag;, 1984

About this Item

342 Seiten Das hier angebotene Buch stammt aus einer teilaufgelösten wissenschaftlichen Bibliothek und trägt die entsprechenden Kennzeichnungen (Rückenschild, Instituts-Stempel.). Einbandkanten sind leicht bestossen; der Buchzustand ist ansonsten ordentlich und dem Alter entsprechend gut. Sprache: Englisch Gewicht in Gramm: 600.

Seller Inventory # 1499139

Bibliographic Details

• Title: Differential Inclusions: Set-Valued Maps and Viability Theory Grundlehren der mathematischen Wissenschaften 264
• Publisher: Springer Verlag
• Publication Date: 1984
• Language: English
• ISBN 10: 3540131051
• ISBN 13: 9783540131052
• Binding: gebundene Ausgabe
• Condition: Gut
• Weight: 600 grams
• Seller catalogs:
  • 200 Mathematik

About this title

Synopsis

A great impetus to study differential inclusions came from the development of Control Theory, i.e. of dynamical systems x'(t) = f(t, x(t), u(t)), x(O)=xo "controlled" by parameters u(t) (the "controls"). Indeed, if we introduce the set-valued map F(t, x)= {f(t, x, u)}ueu then solutions to the differential equations (*) are solutions to the "differen- tial inclusion" (**) x'(t)EF(t, x(t)), x(O)=xo in which the controls do not appear explicitely. Systems Theory provides dynamical systems of the form d x'(t)=A(x(t)) dt (B(x(t))+ C(x(t)); x(O)=xo in which the velocity of the state of the system depends not only upon the x(t) of the system at time t, but also on variations of observations state B(x(t)) of the state. This is a particular case of an implicit differential equation f(t, x(t), x'(t)) = 0 which can be regarded as a differential inclusion (**), where the right-hand side F is defined by F(t, x)= {vlf(t, x, v)=O}. During the 60's and 70's, a special class of differential inclusions was thoroughly investigated: those of the form X'(t)E - A(x(t)), x (0) =xo where A is a "maximal monotone" map. This class of inclusions contains the class of "gradient inclusions" which generalize the usual gradient equations x'(t) = -VV(x(t)), x(O)=xo when V is a differentiable "potential". 2 Introduction There are many instances when potential functions are not differentiable.