A global in time existence and uniqueness result for an integrodifferential hyperbolic inverse problem with memory effect |
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Authors: | Bin Wu Jijun Liu |
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Affiliation: | a Department of Mathematics, Southeast University, Nanjing, 210096, China b College of Mathematics and Physics, Nanjing University of Information Science and Technology, Nanjing 210044, China |
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Abstract: | We consider an inverse problem for a one-dimensional integrodifferential hyperbolic system, which comes from a simplified model of thermoelasticity. This inverse problem aims to identify the displacement u, the temperature η and the memory kernel k simultaneously from the weighted measurement data of temperature. By using the fixed point theorem in suitable Sobolev spaces, the global in time existence and uniqueness results of this inverse problem are obtained. Moreover, we prove that the solution to this inverse problem depends continuously on the noisy data in suitable Sobolev spaces. For this nonlinear inverse problem, our theoretical results guarantee the solvability for the proposed physical model and the well-posedness for small measurement time τ, which is quite different from general inverse problems. |
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Keywords: | Thermoelastic model Memory effect Inverse problem Existence Uniqueness Error estimate |
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