Global Well-Posedness of Solutions to a Class of Double Phase Parabolic Equation With Variable Exponents

The main objective of this paper is to study a class parabolic equation driven by double phase operator with initial-boundary value conditions. As well known, subcritical hypotheses play an important role in investigating well-posedness result and elliptic equations. highlight overcome the difficulties without assumption creates restricting domain. We firstly obtain local solution separately on radial nonradial cases appropriate approach subdifferential, Palais principle symmetric criticality variational methods. Later, using potential method, results global decay estimates energy functional are proved when initial subcritical. Finally, we derived blow-up finite time solutions data satisfies different present work extends complements some earlier contributions related equations involving p(x)-Laplacian.