INVERSE PROBLEMS OF IDENTIFYING THE TIME-DEPENDENT SOURCE COEFFICIENT FOR SUBELLIPTIC HEAT EQUATIONS

Mansur I. Ismailov; Tohru Ozawa; Durvudkhan Suragan

doi:10.3934/ipi.2023056

INVERSE PROBLEMS OF IDENTIFYING THE TIME-DEPENDENT SOURCE COEFFICIENT FOR SUBELLIPTIC HEAT EQUATIONS

Mansur I. Ismailov, Tohru Ozawa, Durvudkhan Suragan

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We discuss inverse problems of determining the time-dependent source coefficient for a general class of subelliptic heat equations. We show that a single data at an observation point guarantees the existence of a (smooth) solution pair for the inverse problem. Moreover, additional data at the observation point implies an explicit formula for the time-dependent source coefficient. We also explore an inverse problem with nonlocal additional data, which seems a new approach even in the Laplacian case.

Original language	English
Pages (from-to)	813-823
Number of pages	11
Journal	Inverse Problems and Imaging
Volume	18
Issue number	4
DOIs	https://doi.org/10.3934/ipi.2023056
Publication status	Published - Aug 2024

Keywords

control parameter
Hörmander vector field
Inverse problem
subelliptic heat equation

ASJC Scopus subject areas

Analysis
Modelling and Simulation
Discrete Mathematics and Combinatorics
Control and Optimization

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10.3934/ipi.2023056

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abstract = "We discuss inverse problems of determining the time-dependent source coefficient for a general class of subelliptic heat equations. We show that a single data at an observation point guarantees the existence of a (smooth) solution pair for the inverse problem. Moreover, additional data at the observation point implies an explicit formula for the time-dependent source coefficient. We also explore an inverse problem with nonlocal additional data, which seems a new approach even in the Laplacian case.",

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AB - We discuss inverse problems of determining the time-dependent source coefficient for a general class of subelliptic heat equations. We show that a single data at an observation point guarantees the existence of a (smooth) solution pair for the inverse problem. Moreover, additional data at the observation point implies an explicit formula for the time-dependent source coefficient. We also explore an inverse problem with nonlocal additional data, which seems a new approach even in the Laplacian case.

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INVERSE PROBLEMS OF IDENTIFYING THE TIME-DEPENDENT SOURCE COEFFICIENT FOR SUBELLIPTIC HEAT EQUATIONS

Abstract

Keywords

ASJC Scopus subject areas

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