Solving an inverse parabolic problem by optimization from final measurement data
Solving an inverse parabolic problem by optimization from final measurement data
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DOI：
10.1016/j.cam.2005.06.003
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发表时间：
2006-08
影响因子：
2.4
通讯作者：
Qun Chen;Jijun Liu
中科院分区：
文献类型：
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作者：
Qun Chen;Jijun Liu
考虑由最终测量u（x，T）重构抛物方程ut-Δu+q（x）u=0中系数q的反问题，其中q在L1（Ω）的某个子集中.采用优化方法，结合有限元法，在一定的假设条件下得到了数值解。证明了极小元的存在性以及近似解在有限维空间中的收敛性。本文的新内容是不需要q上H1-范数的一致先验界。数值实现也被提出。
We consider an inverse problem of reconstructing the coefficient q in the parabolic equation ut-Δu+q(x)u=0 from the final measurement u(x,T), where q is in some subset of L1(Ω). The optimization method, combined with the finite element method, is applied to get the numerical solution under some assumption on q. The existence of minimizer, as well as the convergence of approximate solution in finite-dimensional space, is proven. The new ingredient in this paper is that we do not need uniformly a priori bounds of H1-norm on q. Numerical implementations are also presented.