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Inverse Problems for Fractional Partial Differential Equations.
・ISBN 978-1-4704-7245-0 hard US$ 135.00
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| 著者・編者 | Kaltenbacher, Barbara / Rundell, William, |
|---|---|
| シリーズ | Graduate Studies in Mathematics |
| 出版社 | (American Mathematical Society, US) |
| 出版年月 | 2023 |
| ページ数 | 475 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-869＞ |
解説
As the title of the book indicates, this is primarily a book on partial differential equations (PDEs) with two definite slants: toward inverse problems and to the inclusion of fractional derivatives. The standard paradigm, or direct problem, is to take a PDE, including all coefficients and initial/boundary conditions, and to determine the solution. The inverse problem reverses this approach asking what information about coefficients of the model can be obtained from partial information on the solution. Answering this question requires knowledge of the underlying physical model, including the exact dependence on material parameters.
The last feature of the approach taken by the authors is the inclusion of fractional derivatives. This is driven by direct physical applications: a fractional derivative model often allows greater adherence to physical observations than the traditional integer order case.
The book also has an extensive historical section and the material that can be called ""fractional calculus"" and ordinary differential equations with fractional derivatives. This part is accessible to advanced undergraduates with basic knowledge on real and complex analysis. At the other end of the spectrum, lie nonlinear fractional PDEs that require a standard graduate level course on PDEs.
The last feature of the approach taken by the authors is the inclusion of fractional derivatives. This is driven by direct physical applications: a fractional derivative model often allows greater adherence to physical observations than the traditional integer order case.
The book also has an extensive historical section and the material that can be called ""fractional calculus"" and ordinary differential equations with fractional derivatives. This part is accessible to advanced undergraduates with basic knowledge on real and complex analysis. At the other end of the spectrum, lie nonlinear fractional PDEs that require a standard graduate level course on PDEs.