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.
General
Imprint: |
American Mathematical Society
|
Country of origin: |
United States |
Series: |
Graduate Studies in Mathematics |
Release date: |
June 2023 |
Authors: |
Barbara Kaltenbacher
• William Rundell
|
ISBN-13: |
978-1-4704-7277-1 |
Categories: |
Books
|
LSN: |
1-4704-7277-5 |
Barcode: |
9781470472771 |
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