2017/05/10 by Türker Özsarı, Özsarı, Türker
Mathematics · Physics and Astronomy · #35A01 #35B44 #35Q55 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1705.03965
openalex publication_date 2017/05/10 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
The finite time blow-up of solutions for 1-D NLS with oscillating\nnonlinearities is shown in two domains: (1) the whole real line where the\nnonlinear source is acting in the interior of the domain and (2) the right\nhalf-line where the nonlinear source is placed at the boundary point. The\ndistinctive feature of this work is that the the initial energy is allowed to\nbe non-negative and the momentum is allowed to be infinite in contrast to the\nprevious literature on the blow-up of solutions with time dependent\nnonlinearities. The common finite momentum assumption is removed by using a\ncompactly supported or rapidly decaying weight function in virial identities -\nan idea borrowed from Ogawa-Tsutsumi (1991). At the end of the paper, a\nnumerical example satisfying the theory is provided.\n