Optimal shape design for parabolic partial differential equations 放物型方程式に対する最適形状設計問題
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著者
書誌事項
- タイトル
-
Optimal shape design for parabolic partial differential equations
- タイトル別名
-
放物型方程式に対する最適形状設計問題
- 著者名
-
角谷, 敦, 1963-
- 著者別名
-
カドヤ, アツシ
- 学位授与大学
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千葉大学
- 取得学位
-
理学博士
- 学位授与番号
-
甲第905号
- 学位授与年月日
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1992-03-25
注記・抄録
博士論文
目次
- Table of Contents (3コマ目)
- Preface/p1 (5コマ目)
- Chapter1.Abstract Shape Optimization Problems/p7 (11コマ目)
- 1.1.Introduction/p7 (11コマ目)
- 1.2.Abstract domain optimization problem/p8 (12コマ目)
- 1.3.Examples of domain optimization problem/p10 (14コマ目)
- 1.4.Shape optimization problem on the lateral boundary/p16 (20コマ目)
- Chapter2.Optimal Shape Design in Multi-Phase Stefan Problems/p22 (29コマ目)
- 2.0.Introduction/p22 (29コマ目)
- 2.1.Formulation of an optimization problem and an existence result/p24 (31コマ目)
- 2.2.Problem SP(Ω)/p28 (35コマ目)
- 2.3.Proofs of Theorems 1.1 and 1.2/p31 (38コマ目)
- 2.4.Approximation for P(Oc)/p33 (40コマ目)
- 2.5.Energy estimates for SP[数式]/p36 (43コマ目)
- Chapter3.Optimal Shape Design for Elliptic-Parabolic Equations/p44 (51コマ目)
- 3.0.Introduction/p44 (51コマ目)
- 3.1.Formulation of an optimization problem/p45 (52コマ目)
- 3.2.Problem EP(Ω)/p50 (57コマ目)
- 3.3.Proofs of Theorems 1.1 and 1.2/p54 (61コマ目)
- 3.4.Approximation for P(Oc)/p56 (63コマ目)
- 3.5.Energy estimates for EP[数式]/p59 (66コマ目)
- Chapter4.Shape Optimization on the Lateral Boundary for Multi-Phase Stefan Problem/p65 (72コマ目)
- 4.0.Introduction/p65 (72コマ目)
- 4.1.Formulation of an optimization problem and an existence result/p66 (73コマ目)
- 4.2.Problem SP(Γ)/p72 (79コマ目)
- 4.3.Proofs of Theorems 1.1 and 1.2/p75 (82コマ目)
- 4.4.Approximation for P(IIc)/p78 (85コマ目)
- 4.5.Energy estimates for solutions of [数式]/p82 (89コマ目)
- Appendices/p87 (94コマ目)
- Chapter5.Numerical Computations for Shape Optimization Problems/p92 (99コマ目)
- 5.0.Introduction/p92 (99コマ目)
- 5.1.Numerical results of the domain optimization/p92 (99コマ目)
- 5.2.Numerical results of the domain optimization for Elliptic-Parabolic equations/p97 (104コマ目)
- 5.3.Numerical results of the shape optimization on the lateral boundary/p100 (107コマ目)
- 5.4.Concluding remarks/p104 (111コマ目)