Threshold result for semilinear parabolic equations
Qiuyi Dai, Yonggeng Gu, Fang Liu, Junhui Xie
TL;DR
This paper investigates the initial conditions that determine whether solutions to certain semilinear parabolic equations exist globally or blow up, establishing a threshold based on steady-state solutions.
Contribution
It introduces a new threshold criterion for initial data that predicts the existence or nonexistence of global solutions in semilinear parabolic equations.
Findings
Positive steady-state solutions serve as a threshold for solution behavior.
Initial data above the threshold lead to blow-up, below lead to global existence.
The threshold criterion is rigorously proved for the studied equations.
Abstract
In this paper, we study initial boundary value problem of semilinear parabolic equations and prove that any positive solution of its steady-state problem is an initial datum threshold for the existence and nonexistence of global solution to the above mentioned parabolic problem
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsStability and Controllability of Differential Equations · Nonlinear Partial Differential Equations · Advanced Mathematical Modeling in Engineering