Semigroups of Linear Operators and Applications to Partial Differential Equations

1. Front Matter

   Pages i-x

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2. Generation and Representation

   • A. Pazy

   Pages 1-41

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3. Spectral Properties and Regularity

   • A. Pazy

   Pages 42-75

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4. Perturbations and Approximations

   • A. Pazy

   Pages 76-99

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5. The Abstract Cauchy Problem

   • A. Pazy

   Pages 100-125

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6. Evolution Equations

   • A. Pazy

   Pages 126-182

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7. Some Nonlinear Evolution Equations

   • A. Pazy

   Pages 183-205

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8. Applications to Partial Differential Equations—Linear Equations

   • A. Pazy

   Pages 206-229

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9. Applications to Partial Differential Equations—Nonlinear Equations

   • A. Pazy

   Pages 230-251

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10. Back Matter

    Pages 252-281

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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 the London Mathematical Society#2

• Anfangswertproblem
• Applications
• Equations
• Operatorhalbgruppe
• Operators
• Partielle Differentialgleichung
• Semigroups
• partial differential equation
• wave equation

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 the London Mathematical Society#2

• Planning and Budgeting Committee, Council for Higher Education, Jerusalem, Israel

  A. Pazy

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