Inverse Problems for Fractional Partial Differential Equations by Barbara Kaltenbacher
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.-
Analysis
-
Options Pricing and Portfolio Optimization
-
Scrapbook of Complex Curve Theory
-
Number Theory
-
Inequalities in Matrix Algebras
- Classical Groups and Geometric Algebra
- Partial Differential Equations
-
Algebra
-
A Course on the Web Graph
-
Global Analysis
-
Applied Asymptotic Analysis
-
Advanced Modern Algebra
-
A Course in Operator Theory
-
Representations of Finite and Compact Groups
-
Classical and Quantum Computation
-
Toric Varieties
-
Introduction to Analytic and Probabilistic Number Theory
-
Mathematical Methods in Quantum Mechanics
-
Discovering Modern Set Theory, Part 1
-
Differential Geometry, Lie Groups, and Symmetric Spaces
-
Lectures on Elliptic and Parabolic Equations in Sobolev Spaces
-
Riemann Surfaces by Way of Complex Analytic Geometry
-
Advanced Modern Algebra, Parts 1 and 2
-
Introduction to Quantum Groups and Crystal Bases
-
Introduction to the H-Principle
-
A Course in Differential Geometry
-
Measure Theory and Integration
-
Algebraic Number Fields
-
Algebraic Curves and Riemann Surfaces
-
$\textrm {C}^*$-Algebras and Finite-Dimensional Approximations
-
The Calderon Problem
-
Mathematical Foundations of Deep Learning Models and Algorithms
Barbara Kaltenbacher, University of Klagfurt, Klagenfurt, Austria.
William Rundell, Texas A&M University, College Station, TX.
William Rundell, Texas A&M University, College Station, TX.
| SKU | Unavailable |
| ISBN 13 | 9781470472771 |
| ISBN 10 | 1470472775 |
| Title | Inverse Problems for Fractional Partial Differential Equations |
| Author | Barbara Kaltenbacher |
| Series | Graduate Studies In Mathematics |
| Condition | Unavailable |
| Binding Type | Paperback |
| Publisher | American Mathematical Society |
| Year published | 2023-08-15 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |