Lipschitz stability for an inverse hyperbolic problem of determining two coefficients by a finite number of observations

• We consider an inverse problem of reconstructing two spatially varying coefficients in an acoustic equation of hyperbolic type using interior data of solutions with suitable choices of initial condition. Using a Carleman estimate, we prove Lipschitz stability estimates which ensure unique reconstruction of both coefficients. Our theoretical results are justified by numerical studies on the reconstruction of two unknown coefficients using noisy backscattered data.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

NATURVETENSKAP  -- Matematik -- Beräkningsmatematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Computational Mathematics (hsv//eng)

NATURVETENSKAP  -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Probability Theory and Statistics (hsv//eng)

NATURVETENSKAP  -- Matematik -- Matematisk analys (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Mathematical Analysis (hsv//eng)

Nyckelord

coefficient inverse problem

Carleman estimate

an acoustic equation of hyperbolic type

two space-

arbitrary boundary observation

maxwells equations

logarithmic

stability

limited observations

single measurement

acoustic equation

wave-equation

reconstruction

uniqueness

system

two space-dependent coefficients

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art (ämneskategori)