Existence of renormalized solutions to the parabolic initial-boundary value problems involving variable exponents and measure data

In this paper, we establish the existence of a renormalized solution to the initial-boundary problem to the parabolic differential problem involving variable exponent under the Leray–Lions type of conditions. We show the independence of the definition of the renormalized solution of the decomposition of the given measure, and applying the approximation approach we establish the existence of a renormalized solution to the parabolic problem with measure data, which does not charge the sets of zero capacity.