Finite time blow-up and global solutions for a nonlocal parabolic equation at high energy level

2018/05/02 by Xiaoliang Li, Li, Xiaoliang, Baiyu Liu +1
Engineering · Mathematics · #35K55 #5B44 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1805.00845

openalex publication_date 2018/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the solution of a nonlocal parabolic equation. Focusing on the solutions with initial data at high energy level, we find the criteria for global existence and finite time blow up for the corresponding solution respectively. Moreover, we prove that there always exists blow up solution with negative Nehari functional no matter how large the energy is.

Citations

• Saddle points and instability of nonlinear hyperbolic equations

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