**Graduate Studies in Mathematics**

Volume: 135;
2012;
377 pp;
Hardcover

MSC: Primary 35;

Print ISBN: 978-0-8218-7576-6

Product Code: GSM/135

List Price: $75.00

Individual Member Price: $60.00

**Electronic ISBN: 978-0-8218-8784-4
Product Code: GSM/135.E**

List Price: $75.00

Individual Member Price: $60.00

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#### Supplemental Materials

# Linear and Quasi-linear Evolution Equations in Hilbert Spaces

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*Pascal Cherrier; Albert Milani*

This book considers evolution equations of hyperbolic
and parabolic type. These equations are studied from a common point of view,
using elementary methods, such as that of energy estimates, which prove to be
quite versatile. The authors emphasize the Cauchy problem and present a unified
theory for the treatment of these equations. In particular, they provide local
and global existence results, as well as strong well-posedness and asymptotic
behavior results for the Cauchy problem for quasi-linear equations. Solutions
of linear equations are constructed explicitly, using the Galerkin method; the
linear theory is then applied to quasi-linear equations, by means of a
linearization and fixed-point technique. The authors also compare hyperbolic
and parabolic problems, both in terms of singular perturbations, on compact
time intervals, and asymptotically, in terms of the diffusion phenomenon, with
new results on decay estimates for strong solutions of homogeneous quasi-linear
equations of each type.

This textbook presents a valuable introduction to topics in the theory of
evolution equations, suitable for advanced graduate students. The exposition is
largely self-contained. The initial chapter reviews the essential material from
functional analysis. New ideas are introduced along with their context. Proofs
are detailed and carefully presented. The book concludes with a chapter on
applications of the theory to Maxwell's equations and von Karman's
equations.

#### Table of Contents

# Table of Contents

## Linear and Quasi-linear Evolution Equations in Hilbert Spaces

- Cover Cover11 free
- Title page iii4 free
- Contents vii8 free
- Preface ix10 free
- Chapter 1. Functional framework 120 free
- Chapter 2. Linear equations 7796
- Chapter 3. Quasi-linear equations 119138
- Chapter 4. Global existence 153172
- Chapter 5. Asymptotic behavior 233252
- Chapter 6. Singular convergence 293312
- Chapter 7. Maxwell’s and von Karman’s equations 335354
- List of function spaces 361380
- Bibliography 365384
- Index 375394 free
- Back Cover Back Cover1400

#### Readership

Graduate students and research mathematicians interested in partial differential equations.