Semigroup approach to global well-posedness of the biharmonic Newell-Whitehead-Segel equation. (English) Zbl 1524.31001
Summary: 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, based on 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 \(\mathcal{H}^4\)-norm, it has been that the solution is indeed global in time.
MSC:
| 31A05 | Harmonic, subharmonic, superharmonic functions in two dimensions |
| 47H20 | Semigroups of nonlinear operators |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 31A30 | Biharmonic, polyharmonic functions and equations, Poisson’s equation in two dimensions |
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