Inverse problems for fractional partial differential equations
著者
書誌事項
Inverse problems for fractional partial differential equations
(Graduate studies in mathematics, 230)
American Mathematical Society, c2023
- : paperback
大学図書館所蔵 全1件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Includes bibliographical references (p. 483-502) and index
内容説明・目次
内容説明
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.
目次
Preamble
Genesis of fractional models
Special functions and tools
Fractional calculus
Fractional ordinary differential equations
Mathematical theory of subdiffusion
Analysis of fractionally damped wave equations
Methods for solving inverse problems
Fundamental inverse problems for fractional order models
Inverse problems for fractional diffusion
Inverse problems for fractionally damped wave equations
Outlook beyond Abel
Mathematical preliminaries
Bibliography
Index
「Nielsen BookData」 より