Semigroups of Linear Operators and Applications to Partial Differential Equations

✍ Scribed by A. Pazy (auth.)

• Publisher: Springer-Verlag New York
• Year: 1983
• Tongue: English
• Leaves: 288
• Series: Applied Mathematical Sciences 44
• Edition: 1
• Category: Library

✦ Synopsis

From the reviews: "Since E. Hille and K. Yoshida established the characterization of generators of C0 semigroups in the 1940s, semigroups of linear operators and its neighboring areas have developed into a beautiful abstract theory. Moreover, the fact that mathematically this abstract theory has many direct and important applications in partial differential equations enhances its importance as a necessary discipline in both functional analysis and differential equations. In my opinion Pazy has done an outstanding job in presenting both the abstract theory and basic applications in a clear and interesting manner. The choice and order of the material, the clarity of the proofs, and the overall presentation make this an excellent place for both researchers and students to learn about C0 semigroups." #Bulletin Applied Mathematical Sciences 4/85#1 "In spite of the other monographs on the subject, the reviewer can recommend that of Pazy as being particularly written, with a bias noticeably different from that of the other volumes. Pazy's decision to give a connected account of the applications to partial differential equations in the last two chapters was a particularly happy one, since it enables one to see what the theory can achieve much better than would the insertion of occasional examples. The chapters achieve a very nice balance between being so easy as to appear disappointing, and so sophisticated that they are incomprehensible except to the expert." #Bulletin of theLondon Mathematical Society#2

✦ Table of Contents

Front Matter....Pages i-x
Generation and Representation....Pages 1-41
Spectral Properties and Regularity....Pages 42-75
Perturbations and Approximations....Pages 76-99
The Abstract Cauchy Problem....Pages 100-125
Evolution Equations....Pages 126-182
Some Nonlinear Evolution Equations....Pages 183-205
Applications to Partial Differential Equations—Linear Equations....Pages 206-229
Applications to Partial Differential Equations—Nonlinear Equations....Pages 230-251
Back Matter....Pages 252-281

✦ Subjects

Analysis; Group Theory and Generalizations