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Existence and Uniqueness of an Inverse Memory Kernel for an Integro-Differential Parabolic Equation with Free Boundary

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We consider an inverse problem for an integro-differential parabolic equation with free boundary. This inverse problem aims to identify the memory kernel function from a global measurement data. Based on… Click to show full abstract

We consider an inverse problem for an integro-differential parabolic equation with free boundary. This inverse problem aims to identify the memory kernel function from a global measurement data. Based on a fixed point argument, we derive the local in time existence and uniqueness of our inverse problem. Additionally, we present a numerical experiment.

Keywords: parabolic equation; integro differential; differential parabolic; memory kernel; equation free; free boundary

Journal Title: Journal of Dynamical and Control Systems
Year Published: 2018

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