Evolutionary Integral Equations and Applications

1. Front Matter

   Pages i-xxvi

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2. Equations of Scalar Type

   1. Front Matter

      Pages 29-29

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   2. Resolvents

      • Jan Prüss

      Pages 30-48

   3. Analytic Resolvents

      • Jan Prüss

      Pages 49-67

   4. Parabolic Equations

      • Jan Prüss

      Pages 68-89

   5. Subordination

      • Jan Prüss

      Pages 90-121

   6. Linear Viscoelasticity

      • Jan Prüss

      Pages 122-150

3. Nonscalar Equations

   1. Front Matter

      Pages 151-151

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   2. Hyperbolic Equations of Nonscalar Type

      • Jan Prüss

      Pages 152-184

   3. Nonscalar Parabolic Equations

      • Jan Prüss

      Pages 185-211

   4. Parabolic Problems in L ^p-Spaces

      • Jan Prüss

      Pages 212-235

   5. Viscoelasticity and Electrodynamics with Memory

      • Jan Prüss

      Pages 236-254

4. Equations on the Line

   1. Front Matter

      Pages 255-255

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   2. Integrability of Resolvents

      • Jan Prüss

      Pages 256-283

   3. Limiting Equations

      • Jan Prüss

      Pages 284-305

   4. Admissibility of Function Spaces

      • Jan Prüss

      Pages 306-322

   5. Further Applications and Complements

      • Jan Prüss

      Pages 323-345

5. Back Matter

   Pages 347-369

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During the last two decades the theory of abstract Volterra equations has under­ gone rapid development. To a large extent this was due to the applications of this theory to problems in mathematical physics, such as viscoelasticity, heat conduc­ tion in materials with memory, electrodynamics with memory, and to the need of tools to tackle the problems arising in these fields. Many interesting phenomena not found with differential equations but observed in specific examples of Volterra type stimulated research and improved our understanding and knowledge. Al­ though this process is still going on, in particular concerning nonlinear problems, the linear theory has reached a state of maturity. In recent years several good books on Volterra equations have appeared. How­ ever, none of them accounts for linear problems in infinite dimensions, and there­ fore this part of the theory has been available only through the - meanwhile enor­ mous - original literature, so far. The present monograph intends to close this gap. Its aim is a coherent exposition of the state of the art in the linear theory. It brings together and unifies most of the relevant results available at present, and should ease the way through the original literature for anyone intending to work on abstract Volterra equations and its applications. And it exhibits many prob­ lems in the linear theory which have not been solved or even not been considered, so far.

• differential equation
• ergodic theory
• function space
• hyperbolic equation
• Integral
• Integral equation

• Universität-GH Paderborn, Paderborn, Germany

  Jan Prüss

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