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Global uniqueness of an inverse problem for stochastic degenerate wave equation with three unknowns. (English) Zbl 1479.35960

Summary: This paper concerns an inverse problem for a stochastic degenerate wave equation. This inverse problem aims to determine a source term and an initial displacement and an initial velocity from the boundary observation and the final time observation. More precisely, we will prove a global uniqueness for our inverse problem by a suitable Carleman estimate for the stochastic degenerate wave equation.

MSC:

35R30 Inverse problems for PDEs
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
35L20 Initial-boundary value problems for second-order hyperbolic equations
35R60 PDEs with randomness, stochastic partial differential equations
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
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