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Article detail · 2001

Global Lipschitz stability in an inverse hyperbolic problem by interior observations

Journal

Inverse Problems
OpenAlex Open access · bronze SJR Q1 JCR Q1 Citations 216 Top 10% Percentile 96.0% FWCI 5.22
Year
2001
DOI
10.1088/0266-5611/17/4/310
Type
article

Data source split

  • YÖKSİS venue Inverse Problems
  • OpenAlex OpenAlex enrichment (abstract, citations, topics)

OpenAlex record

Abstract

OpenAlex · English

For the solution u ( p ) = u ( p )( x , t ) to ∂ t 2 u ( x , t )-Δ u ( x , t )- p ( x ) u ( x , t ) = 0 in Ω × (0, T ) and (∂ u /∂ν)| ∂Ω × (0, T ) = 0 with given u (·,0) and ∂ t u (·,0), we consider an inverse problem of determining p ( x ), x ∊Ω, from data u |ω × (0, T ) . Here Ω⊂ n , n = 1,2,3, is a bounded domain, ω is a sub-domain of Ω and T >0. For suitable ω⊂Ω and T >0, we prove an upper and lower estimate of Lipschitz type between || p - q || L 2 (Ω) and ||∂ t ( u ( p )- u ( q ))|| L 2 (ω × (0, T )) + ||∂ t 2 ( u ( p )- u ( q ))|| L 2 (ω × (0, T )) .

Topics

Citations

OpenAlex cited_by_count. Not a WoS or Scopus citation count; those sources have no separate column here.

216 citations

OpenAlex cited_by_count (cache / database)

77 publications in the local catalog that cite this work (OpenAlex reference match; not the full global list).

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  2. Coefficient inverse problem for a fractional diffusion equation 2013 Citations 123 · OpenAlex
  3. Determination of a coefficient in an acoustic equation with a single measurement 2003 Citations 116 · OpenAlex
  4. An inverse problem for the dynamical Lamé system with two sets of boundary data 2003 Citations 92 · OpenAlex
  5. Lipschitz stability of an inverse problem for an acoustic equation 2006 Citations 86 · OpenAlex
  6. Logarithmic stability in determination of a coefficient in an acoustic equation by arbitrary boundary observation 2005 Citations 70 · OpenAlex
  7. Determination of source terms in a degenerate parabolic equation 2010 Citations 65 · OpenAlex
  8. Inverse problem for a parabolic system with two components by measurements of one component 2009 Citations 62 · OpenAlex
  9. Carleman estimates for the non-stationary Lamé system and the application to an inverse problem 2004 Citations 62 · OpenAlex
  10. Lipschitz stability in the determination of the principal part of a parabolic equation 2009 Citations 56 · OpenAlex

Authors

No author information.