Open AccessLifespan of solutions to a parabolic type Kirchhoff equation with time-dependent nonlinearity
Author(s) -
Haixia Li
Publication year - 2021
Publication title -
evolution equations and control theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 19
eISSN - 2163-2480
pISSN - 2163-2472
DOI - 10.3934/eect.2020088
Subject(s) - mathematics , nonlinear system , mathematical analysis , type (biology) , boundary value problem , parabolic partial differential equation , initial value problem , energy (signal processing) , energy method , physics , partial differential equation , quantum mechanics , ecology , statistics , biology
In this paper, an initial boundary value problem for a parabolic type Kirchhoff equation with time-dependent nonlinearity is considered. A new blow-up criterion for nonnegative initial energy is given and upper and lower bounds for the blow-up time are also derived. These results partially generalize some recent ones obtained by Han and Li in [Threshold results for the existence of global and blow-up solutions to Kirchhoff equations with arbitrary initial energy, Computers and Mathematics with Applications, 75(2018), 3283-3297].