A global in time existence and uniqueness result of a multidimensional inverse problem

ABSTRACT

This study is the multidimensional inverse problem for a viscoelasticity equation. This inverse problem aims to reconstruct the displacement and convolutional kernel of the integral term simultaneously, from the measurement described as the overdetermination condition. The main result is the theorem of global unique solvability of the inverse problem in the class of functions continuously in the time variable t and analytic in the space variable. The methods of scales of Banach spaces of real analytic functions of variable and weight norms in the class of continuous functions are applied.

KEYWORDS:

• Inverse problem
• global solvability
• viscoelasticity equation
• Banach space
• weight norm

AMS MATHEMATICS SUBJECT CLASSIFICATIONS:

• 35K10
• 45G10

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Ministry of Science and Higher Education of the Russian Federation [Grant/Award Number: 075-02-2023-914].