Lifespan of solutions to a parabolic type Kirchhoff equation with time-dependent nonlinearity | Zendy

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Lifespan of solutions to a parabolic type Kirchhoff equation with time-dependent nonlinearity

Author(s) -

Haixia Li

Publication year - 2020

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].

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