Open AccessBlow-up analysis for a reaction-diffusion equation with gradient absorption terms
Author(s) -
Mengyang Liang,
Zhong Bo Fang,
Su-Cheol Yi
Publication year - 2021
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2021800
Subject(s) - mathematics , absorption (acoustics) , mathematical analysis , diffusion , measure (data warehouse) , reaction–diffusion system , flux (metallurgy) , nonlinear system , diffusion equation , boundary value problem , chemistry , physics , thermodynamics , optics , computer science , quantum mechanics , economy , organic chemistry , database , economics , service (business)
This paper deals with the blow-up phenomena of solution to a reaction-diffusion equation with gradient absorption terms under nonlinear boundary flux. Based on the technique of modified differential inequality and comparison principle, we establish some conditions on nonlinearities to guarantee the solution exists globally or blows up at finite time. Moreover, some bounds for blow-up time are derived under appropriate measure in higher dimensional spaces $ \left({N \ge 2} \right). $