2018/05/17 by Tej‐Eddine Ghoul, Ghoul, Tej-Eddine, Van Tien Nguyen +3 · 2 citations
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.1805.06616
openalex publication_date 2018/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the higher-order semilinear parabolic equation
partialt u =\n-(-
Delta)m u + u|u|p-1, in the whole space \ℝN, where p >\n1 and m \≥ 1 is an odd integer. We exhibit type I non self-similar blowup\nsolutions for this equation and obtain a sharp description of its asymptotic\nbehavior. The method of construction relies on the spectral analysis of a non\nself-adjoint linearized operator in an appropriate scaled variables setting. In\nview of known spectral and sectorial properties of the linearized operator\nobtained by [Galaktionov, rspa2011], we revisit the technique developed by\n[Merle-Zaag, duke1997] for the classical case m = 1, which consists in two\nsteps: the reduction of the problem to a finite dimensional one, then solving\nthe finite dimensional problem by a classical topological argument based on the\nindex theory. Our analysis provides a rigorous justification of a formal result\nin [Galaktionov, rspa2011].\n