Differential Inclusions: Set-Valued Maps and Viability Theory (Grundlehren Der Mathematischen Wissenschaften)

Aubin, J. -P.

ISBN 10: 3540131051 / ISBN 13: 9783540131052

Edité par Springer-Verlag Berlin And Heidelberg Gmbh & Co. K, 1984

A propos de cet article

This is an ex-library book and may have the usual library/used-book markings inside.This book has hardback covers. In good all round condition. No dust jacket. Please note the Image in this listing is a stock photo and may not match the covers of the actual item,700grams, ISBN:3540131051.

N° de réf. du vendeur 5848371

Détails bibliographiques

• Titre: Differential Inclusions: Set-Valued Maps and Viability Theory (Grundlehren Der Mathematischen Wissenschaften)
• Éditeur: Springer-Verlag Berlin And Heidelberg Gmbh & Co. K
• Date de parution: 1984
• Langue: anglais
• ISBN à 10 chiffres: 3540131051
• ISBN à 13 chiffres: 9783540131052
• Reliure: Couverture rigide
• État de l'article: Good
• Catalogues du vendeur:
  • German Language & Literature

A propos de ce titre

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.