Inverse problems for subdiffusion equations and approximation results

Simone Creo; Maria Rosaria Lancia; Gianluca Mola; Silvia Romanelli; Simone Creo; Maria Rosaria Lancia; Gianluca Mola; Silvia Romanelli

doi:10.3934/math.2026934

AIMS Mathematics

2026, Volume 11, Issue 7: 23173-23198. doi: 10.3934/math.2026934

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Inverse problems for subdiffusion equations and approximation results

1.
Dipartimento di Scienze di Base e Applicate per l'Ingegneria, Sapienza Università di Roma, via A. Scarpa 16, 00161 Roma, Italy
2.
Department of Science and Engineering, Sorbonne University Abu Dhabi, Al Reem Island, 38044 Abu Dhabi, UAE
3.
Dipartimento di Matematica, Università degli Studi di Bari Aldo Moro, via E. Orabona 4, 70125 Bari, Italy

Received: 18 May 2026 Revised: 16 July 2026 Accepted: 21 July 2026 Published: 30 July 2026
MSC : 35B40, 35K20, 35R11, 35R30, 47B25, 47D06

The aim of this paper is to investigate time-fractional inverse problems involving a self-adjoint operator $ A $ and their approximations. We prove existence and uniqueness results for the solution of the inverse problem consisting of the identification of a single constant conductivity, under overdeterminating conditions of energy type. Then we study their approximations in terms of suitable inverse problems via the Mosco convergence of the associated energies. Some applications to boundary value problems are also presented.
- inverse problems,
- Mosco convergence,
- fractional time derivatives,
- evolution equations in Hilbert spaces,
- resolvent families
Citation: Simone Creo, Maria Rosaria Lancia, Gianluca Mola, Silvia Romanelli. Inverse problems for subdiffusion equations and approximation results[J]. AIMS Mathematics, 2026, 11(7): 23173-23198. doi: 10.3934/math.2026934

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Abstract

The aim of this paper is to investigate time-fractional inverse problems involving a self-adjoint operator $ A $ and their approximations. We prove existence and uniqueness results for the solution of the inverse problem consisting of the identification of a single constant conductivity, under overdeterminating conditions of energy type. Then we study their approximations in terms of suitable inverse problems via the Mosco convergence of the associated energies. Some applications to boundary value problems are also presented.

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