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Carleman estimate for stochastic degenerate wave equation with drift and its application

  • Lin Yan EMAIL logo and Bin Wu
Published/Copyright: July 1, 2025

Abstract

This paper is devoted to establishing the Carleman estimate for the stochastic degenerate wave equation with drift in the weakly degenerate case. Due to the degeneracy, we first study an approximate nondegenerate system. In order to overcome the difficulty arising from the drift term, we introduce an auxiliary function by which the diffusion and the drift term are transformed into a complex whole. After complicated and detailed estimates, we then derive the Carleman estimate for the stochastic degenerate wave equation. As an application for our Carleman estimate, we solve an inverse problem of determining three unknowns simultaneously by some suitable observations for the stochastic degenerate wave equation with drift. More precisely, we obtain a global uniqueness result for our inverse problem.

MSC 2020: 35L05; 60H15; 35R30; 35A02

Award Identifier / Grant number: 12171248

Funding statement: This work is supported by NSFC (No. 12171248).

Acknowledgements

The authors gratefully thank the associate editor and the anonymous referees for their valuable comments and suggestions for improving this paper.

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Received: 2024-08-22
Revised: 2025-05-21
Accepted: 2025-06-03
Published Online: 2025-07-01
Published in Print: 2025-08-01

© 2025 Walter de Gruyter GmbH, Berlin/Boston

Downloaded on 10.12.2025 from https://www.degruyterbrill.com/document/doi/10.1515/jiip-2024-0060/pdf
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