Inverse Problems for Fractional Partial Differential Equations (Graduate Studies in Mathematics)

Barbara Kaltenbacher; William Rundell

ISBN 10: 1470472775 / ISBN 13: 9781470472771

Published by American Mathematical Society, 2023

About this Item

Seller Inventory # 26396644545

Bibliographic Details

• Title: Inverse Problems for Fractional Partial Differential Equations (Graduate Studies in Mathematics)
• Publisher: American Mathematical Society
• Publication Date: 2023
• Language: English
• ISBN 10: 1470472775
• ISBN 13: 9781470472771
• Binding: Soft cover
• Condition: New

About this title

Synopsis

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.

About the Author

Barbara Kaltenbacher, University of Klagfurt, Klagenfurt, Austria, and William Rundell, Texas A&M University, College Station, TX