An investigation of an inverse problem for second-order abstract differential equation

In this manuscript, we consider an inverse problem for a second-order abstract differential equation in a Banach space and identify the parameter using an over-determined condition on a mild solution. A direct approach using Volterra integral equation for sufficiently regular data and an optimal control approach for less regular data are the main techniques to find the solution pair of the considered problem. Finally, an application to an inverse problem that appears in elasticity theory is presented.

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This manuscript investigates an inverse problem for a second-order abstract differential equation in a Banach space, where the parameter is identified using an over-determined condition on a mild solution. The main techniques to find the solution pair of the considered problem are a direct approach using Volterra integral equation for sufficiently regular data and an optimal control approach for less regular data. An application to an inverse problem in elasticity theory is also presented.