Determination of the body force of a two-dimensional isotropic elastic body

Dang Duc Trong (1) , Alain Pham Ngoc Dinh (2) , Phan Thanh Nam (1) , Truong Trung Tuyen (3)

1 UNS-HCMC - Mathematics Department
2 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
3 IU - Department of Mathematics

Let $\Omega$ represent a two$-$dimensional isotropic elastic body. We consider the problem of determining the body force $F$ whose form $\varphi(t)(f_1(x),f_2(x))$ with $\varphi$ be given inexactly. The problem is nonlinear and ill-posed. Using the Fourier transform, the methods of Tikhonov's regularization and truncated integration, we construct a regularized solution from the data given inexactly and derive the explicitly error estimate.

Mots clés: body force; elastic body; Fourier transform; ill$-posed problem; Tikhonov's regularization; truncated integration

Domaines: Equations aux dérivées partielles [math.AP]

Dang Duc Trong, Alain Pham Ngoc Dinh, Phan Thanh Nam, Truong Trung Tuyen. Determination of the body force of a two-dimensional isotropic elastic body. 2007. ⟨hal-00146732v1⟩