An inverse coefficient problem for a parabolic hemivariational inequality

Abstract

We consider a class of identification problems for a non-linear parabolic boundary hemivariational inequality. Using the least square cost functionals, the problem is to identify an unknown coefficient which depends on the gradient of the solution. It is shown that the hemivariational inequality admits a unique weak solution, which depends continuously on the coefficient. The boundary condition is of a subdifferential type with non-convex and non-smooth potential. Existence of solutions to the inverse problems is established by using the direct method.

Keywords:

• parabolic
• inverse
• identification
• non-convex
• hemivariational inequality
• coefficient
• Clarke subdifferential
• weak solution

AMS Subject Classifications::

• 35K85
• 35R30
• 49J20

Acknowledgement

This research was supported in part by the Ministry of Science and Higher Education of Poland under Grant no. N201 027 32/1449.