### Abstract

We consider the higher-order semilinear parabolic equation α_{t}u=-(-Δ)^{m}u+u|u|^{p-1}, in the whole space ℝ^{N}, where p > 1 and m ≥ 1 is an odd integer. We exhibit type I non self-similar blowup solutions for this equation and obtain a sharp description of its asymptotic behavior. The method of construction relies on the spectral analysis of a non self-adjoint linearized operator in an appropriate scaled variables setting. In view of known spectral and sectorial properties of the linearized operator obtained by Galaktionov [15], we revisit the technique developed by Merle-Zaag [23] for the classical case m = 1, which consists in two steps: the reduction of the problem to a finite dimensional one, then solving the finite dimensional problem by a classical topological argument based on the index theory. Our analysis provides a rigorous justification of a formal result in [15].

Original language | English (US) |
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Pages (from-to) | 388-412 |

Number of pages | 25 |

Journal | Advances in Nonlinear Analysis |

Volume | 9 |

Issue number | 1 |

DOIs | |

State | Published - Mar 1 2019 |

### Keywords

- Blowup profile
- Blowup solution
- Higher order parabolic equation
- Stability

### ASJC Scopus subject areas

- Analysis

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## Cite this

*Advances in Nonlinear Analysis*,

*9*(1), 388-412. https://doi.org/10.1515/anona-2020-0006