Nonlinear Differential Equations of Monotone Types in Banach Spaces

2010. Auflage 2010
ISBN: 978-1-4419-5541-8
Verlag: Springer

Buch, Englisch, 272 Seiten, Format (B × H): 167 mm x 241 mm, Gewicht: 1270 g

Reihe: Springer Monographs in Mathematics

In the last decades, functional methods played an increasing role in the qualita tive theory of partial differential equations. The spectral methods and theory of C 0 semigroups of linear operators as well as Leray–Schauder degree theory, ?xed point theorems, and theory of maximal monotone nonlinear operators are now essential functional tools for the treatment of linear and nonlinear boundary value problems associated with partial differential equations. An important step was the extension in the early seventies of the nonlinear dy namics of accretive (dissipative) type of the Hille–Yosida theory of C semigroups 0 of linear continuous operators. The main achievement was that the Cauchy problem associated with nonlinear m accretive operators in Banach spaces is well posed and the corresponding dynamic is expressed by the Peano exponential formula from ?nite dimensional theory. This fundamental result is the corner stone of the whole existence theory of nonlinear in?nite dynamics of dissipative type and its contri bution to the development of the modern theory of nonlinear partial differential equations cannot be underestimated.

Zielgruppe

Research

Autoren/Hrsg.

Barbu, Viorel

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

Fundamental Functional Analysis.- Maximal Monotone Operators in Banach Spaces.- Accretive Nonlinear Operators in Banach Spaces.- The Cauchy Problem in Banach Spaces.- Existence Theory of Nonlinear Dissipative Dynamics.