The body force in a three-dimensional Lame' system: identification and regularization

Dang Duc Trong; Phan Thanh Nam; Phung Trong Thuc

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arXiv · 1103.1536

The body force in a three-dimensional Lame' system: identification and regularization

Dang Duc Trong·Phan Thanh Nam·Phung Trong Thuc

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Abstract

Let a three-dimensional isotropic elastic body be described by the Lam\'e system with the body force of the form $F(x,t)=\phi(t)f(x)$, where $\phi$ is known. We consider the problem of determining the unknown spatial term $f(x)$ of the body force where the surface stress history is given as the overdetermination. This inverse problem is ill-posed. Using the interpolation method and truncated Fourier series, we construct a regularized solution from approximate data and provide explicit error estimates. AMS 2010 Subject Classification: 35L20, 35R30. Keywords: Body force, elastic, ill$-$posed problem, interpolation, Fourier series.

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Dang Duc Trong, Phan Thanh Nam, Phung Trong Thuc. 2011-03-08. The body force in a three-dimensional Lame' system: identification and regularization. https://arxiv.org/abs/1103.1536

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