Mathematical Analysis of Continuum Mechanics and Industrial Applications III

1. Front Matter

   Pages i-viii

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2. Fracture Mechanics and Radiative Transport

   1. Front Matter

      Pages 1-1

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   2. Dynamic Unilateral Contact Problem with Averaged Friction for a Viscoelastic Body with Cracks

      • Atusi Tani

      Pages 3-21

   3. Some Recent Results on Regularity of the Crack-tip/Crack-front of Mumford–Shah Minimizers

      • Hayk Mikayelyan

      Pages 23-33

   4. Piecewise Constant Upwind Approximations to the Stationary Radiative Transport Equation

      • Hiroshi Fujiwara

      Pages 35-45

3. Elasticity

   1. Front Matter

      Pages 47-47

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   2. The Mechanics and Mathematics of Bodies Described by Implicit Constitutive Equations

      • K. R. Rajagopal

      Pages 49-65

   3. On the Perturbation of Bleustein–Gulyaev Waves in Piezoelectric Media

      • Gen Nakamura, Kazumi Tanuma, Xiang Xu

      Pages 67-79

   4. Deformation Problem for Glued Elastic Bodies and an Alternative Iteration Method

      • Masato Kimura, Atsushi Suzuki

      Pages 81-94

4. Shape Optimization and Inverse Problems

   1. Front Matter

      Pages 95-95

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   2. Shape Differentiability of Lagrangians and Application to Overdetermined Problems

      • Victor A. Kovtunenko, Kohji Ohtsuka

      Pages 97-110

   3. Identification of an Unknown Shear Force in Euler–Bernoulli Beam Based on Boundary Measurement of Rotation

      • Alemdar Hasanov Hasanoglu

      Pages 111-123

   4. Shape Optimization of Flow Fields Considering Proper Orthogonal Decomposition

      • Takashi Nakazawa

      Pages 125-145

   5. Topology Optimization for Porous Cooling Systems

      • Kentaro Yaji

      Pages 147-156

5. Earthquakes and Tsunamis

   1. Front Matter

      Pages 157-157

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   2. Quasi-static Simulation Method of Earthquake Cycles Based on Viscoelastic Finite Element Modeling

      • Ryoichiro Agata, Takane Hori, Sylvain D. Barbot, Mamoru Hyodo, Tsuyoshi Ichimura

      Pages 159-169

   3. Friction Versus Damage: Dynamic Self-similar Crack Growth Revisited

      • Shiro Hirano

      Pages 171-179

   4. Isobe–Kakinuma Model for Water Waves

      • Tatsuo Iguchi

      Pages 181-191

   5. Tsunami-Height Reduction Using a Very Large Floating Structure

      • Taro Kakinuma, Naoto Ochi

      Pages 193-202

6. Back Matter

   Pages 203-204

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This book focuses on mathematical theory and numerical simulation related to various areas of continuum mechanics, such as fracture mechanics, (visco)elasticity, optimal shape design, modelling of earthquakes and Tsunami waves, material structure, interface dynamics and complex systems. Written by leading researchers from the fields of applied mathematics, physics, seismology, engineering, and industry with an extensive knowledge of mathematical analysis, it helps readers understand how mathematical theory can be applied to various phenomena, and conversely, how to formulate actual phenomena as mathematical problems. 

This book is the sequel to the proceedings of the International Conference of Continuum Mechanics Focusing on Singularities (CoMFoS) 15 and CoMFoS16.

• Continuum Mechanics
• Dynamic Fracture
• Mathematical Modeling
• Shape Optimization and Inverse Problems
• Seismic Waves
• (Visco) Elasticity
• Earthquake and Tsunami
• CoMFoS18

“The proceedings with their industrial applications are of special importance in engineering, and they could be recommended to engineers, researchers and scientists.” (M. Cengiz Dökmeci, zbMATH 1482.74006, 2022)

• Department of Mathematics, Tokyo University of Science, Tokyo, Japan

  Hiromichi Itou

• College of Science and Engineering, Ritsumeikan University, Kusatsu, Japan

  Shiro Hirano

• Faculty of Mathematics and Physics, Kanazawa University, Kanazawa, Japan

  Masato Kimura

• NAWI Graz, Institut für Mathematik, Karl-Franzens University of Graz, Graz, Austria

  Victor A. Kovtunenko

• Siberian Branch of RAS, Lavrentyev Institute of Hydrodynamics, Novosibirsk, Russia

  Alexandr M. Khludnev

Hiromichi Itou is Associate Professor in the Department of Mathematics at the Tokyo University of Science. He is a representative member of The Japan Society for Industrial and Applied Mathematics (JSIAM). His research interests lie in the areas of Fracture Mechanics, Singular integral equations, Analysis of singularities of corner and crack, theory of elasticity, Inverse problems.




Shiro Hirano is Assistant professor in the College of Science and Engineering at the Ritsumeikan University. His research interests lie in the areas of Mathematical modeling of earthquake fault mechanics, Data analysis of seismicity, Laboratory seismology, Earthquake engineering.





Masato Kimura is the Full Professor in the Faculty of Mathematics and Physics at the Kanazawa University. He is a representative member of The Japan Society for Industrial and Applied Mathematics (JSIAM) and a leader of analysis group in Kanazawa Mathematics and mathematical science Research Group (KMRG). His research interests include moving boundary problems (mean curvature flow, Hele-Shaw problem, Stefan problem etc.), numerical analysis for PDE (FDM, FEM, BEM etc.) singular perturbation for elliptic eigenvalue problems with large drift, crack problems in fracture mechanics, shape derivative and its application, bulk-surface system, inverse Cauchy transform of domains, pattern formation in reaction diffusion systems, mathematical analysis of particle methods.





Victor A. Kovtunenko, PhD (1997), Habilitation (2007) is working at the Lavrentyev Institute of Hydrodynamics of the Siberian Division of the Russian Academy of Sciences, and at the Austrian Academy of Sciences (OeAW). He currently serves as a Project Leader of the Austrian Science Foundation (FWF) at the Institute for Mathematics and Scientific Computing at the University of Graz. His research interests include variational inequalities, shape and topology optimization, nonsmooth and numerical optimization, applications to solid mechanics.





Alexandr M. Khludnev is a head of laboratory at the Lavrentyev Institute of Hydrodynamics of the Siberian Division of the Russian Academy of Sciences. Simultaneously he has a part time professor position at Novosibirsk State University. His research interests include variational inequalities, shape and topology optimization, crack problems, contact and free boundary problems in solid mechanics.

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