Semigroup Approach to Global Well-Posedness of the Biharmonic Newell-Whitehead-Segel Equation

The aim of the paper is to establish the global well-posedness of the Newell-Whitehead-Segel Equation driven by the biharmonic operator with Dirichlet boundary conditions through the semigroup method based on the Hille-Yosida Theorem. In particular, using the blow-up criterion we first demonstrate that there exists a unique local maximal classical solution. Next, by showing that the semiflow generated is uniformly bounded in H^4 -norm, it has been that the solution is indeed global in time.