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.