Blow-up solutions for L2 supercritical gKdV equations with exactly k blow-up points. (12th July 2017)

• Record Type: Journal Article
• Authors: Lan, Yang
• Is Part Of: Nonlinearity. Volume 30:Number 8(2017:Aug.)
• Page Start: 3203
• Page End: 3240
• Publication Date: 2017-07-12
• Subjects: KdV -- supercritical -- blow-up -- multiple blow-up points; 35Q53 -- 35B40 -- 35B44; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/aa7765
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: In this paper we consider the slightly L 2 -supercritical gKdV equations ∂ t u + ( u x x + u | u | p − 1 ) x = 0, with the nonlinearity 5 < p < 5 + ε and 0 < ε ≪ 1 . In the previous work of the author, we know that there exists a stable self-similar blow-up dynamics for slightly L 2 -supercritical gKdV equations. Such solutions can be viewed as solutions with a single blow-up point. In this paper we will prove the existence of solutions with multiple blow-up points, and give a description of the formation of the singularity near the blow-up time.