Local well-posedness and blow-up solutions of a fourth-order pseudo-parabolic equation

In this study, the initial and periodic boundary value problem were solved for the following fourthorder pseudo-parabolic equation with gradient non-linearity and pseudo-termwhere a 0. A local existence-uniqueness result for mild solutions was found for any initial data in L 2 ( ) W .In addition, the existence of blow-up solutions was proved and a lower bound for the blow-up time was obtained.