2014 Fiscal Year Final Research Report
Elucidation of fracture phenomena from the viewpoint of singularity of solutions of partial differential equations at crack tips
| Project/Area Number |
23740101
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Basic analysis
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| Research Institution | Tokyo University of Science (2013)
Gunma University (2011-2012) |
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Principal Investigator |
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| Project Period (FY) |
2011 – 2014
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| Keywords | き裂 / 非線形弾性体 / 粘弾性体 / 剛性介在物 / 逆問題 |
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| Outline of Final Research Achievements |
With application of fracture phenomena in mind, we studied the behavior of solutions of partial differential equations at crack tips. In a case of nonlinear equations we did not achieve anything new, but we found a toehold to solve the problem. In a case of boundary value problems in two dimensional elasticity with rigid line inclusions, we proved the existence and uniqueness of the solution and derived the convergent series expansion of the solution near the tip of the rigid inclusion. As an application of this study, we considered a reconstruction problem for cavities in three dimensional linear viscoelasticity, and we established a formula extracting three kinds of information about the unknown cavity from measured data on the boundary.
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| Free Research Field |
偏微分方程式
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