This chapter focuses on inverse problems for stochastic hyperbolic equations. We investigate the determination of unknown initial data and source terms from partial observations, including boundary, terminal, and internal measurements. For the problems considered, we address uniqueness, stability, and reconstruction. Our analysis is based on Carleman estimates derived from a fundamental pointwise weighted identity, and the chapter concludes with several related open problems.

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Inverse Problems for Stochastic Hyperbolic Equations

  • Qi Lü,
  • Yu Wang

摘要

This chapter focuses on inverse problems for stochastic hyperbolic equations. We investigate the determination of unknown initial data and source terms from partial observations, including boundary, terminal, and internal measurements. For the problems considered, we address uniqueness, stability, and reconstruction. Our analysis is based on Carleman estimates derived from a fundamental pointwise weighted identity, and the chapter concludes with several related open problems.