This chapter focuses on inverse problems for stochastic parabolic equations. We study the determination of unknown initial data and source terms from partial observations, including internal, terminal, and boundary measurements. We analyze uniqueness, stability, and reconstruction results. The main results are derived via Carleman estimates based on a fundamental weighted identity, and several related open problems are briefly discussed.

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Inverse Problems for Stochastic Parabolic Equations

  • Qi Lü,
  • Yu Wang

摘要

This chapter focuses on inverse problems for stochastic parabolic equations. We study the determination of unknown initial data and source terms from partial observations, including internal, terminal, and boundary measurements. We analyze uniqueness, stability, and reconstruction results. The main results are derived via Carleman estimates based on a fundamental weighted identity, and several related open problems are briefly discussed.