The existence of solutions for parabolic problem with the limiting case of double phase flux

In the present paper, we are concerned with the existence result to a class of nonlinear parabolic equations driven by the so-called double phase operator in the limiting case with initial boundary value. Under the framework of Musielak-Orlicz Sobolev spaces, we established energy estimates. And by passing the limit of a sequence of solutions of double-phase problems whose highest exponent approximates 1, we obtain that the desired result is a bounded variation solution.