一类带有非奇异主部系数矩阵的2×2强耦合偏微分系统的卡勒曼估计及其反源问题

Abstract

Abstract: We study a Carleman estimate for a 2×2 strongly coupled partial differential system with nonsingular coefficient matrix of principal parts. Different from the method to prove Carleman estimate for a strongly coupled hyperbolic system as in[7] and[15], we first establish a pointwise Carleman estimate by considering two equations in the governing system as a whole rather than by using diagonalization of the system. Furthermore, we prove a global Carleman estimate for this kind of strongly coupled differential system. Finally, as an application, we establish a Hölder stability for an inverse problem of determining two source functions by the boundary observation data.

Key words: Carleman estimate, Strongly coupled system, Inverse source problem, Hölder stability

CLC Number:

O175.28

Wu Bin, Gao Ying, Yan Lin, Yu Jun. Carleman Estimate for a 2×2 Strongly Coupled Partial Differential System with Nonsingular Coefficient Matrix of Principal Parts and Application to an Inverse Source Problem[J].Acta mathematica scientia,Series A, 2018, 38(4): 779-799.

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References 40

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Carleman Estimate for a 2×2 Strongly Coupled Partial Differential System with Nonsingular Coefficient Matrix of Principal Parts and Application to an Inverse Source Problem

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