Affiliation:
1. Department of Mathematics Central University of Kerala Kasaragod Kerala India
Abstract
This article deals with a fourth‐order pseudo‐parabolic partial differential equation with logarithmic nonlinearity. We adopt the Faedo–Galerkin method to analyze the global existence of weak solutions and discuss the existence of a solution in subcritical and critical initial energy situations. Further, applying the concavity approach, we have shown that the solution blows up when the initial energy is subcritical, critical, and supercritical. Moreover, we have provided an upper and lower bound for blow‐up time and a decay estimate for the global solutions.
Funder
Council of Scientific and Industrial Research, India