Non-simultaneous blowup in heat equations with nonstandard growth conditions

Liu, Bingchen; Li, Fengjie

doi:10.1016/j.jde.2012.01.001

Cited by 3 publications

(1 citation statement)

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“…It should be remarked here that paper [16] not only focuses on initial-boundary value problem of (3), but also discusses initial value problem of (3) (Ω = R N ). Since then, many scholars in succession generalize results of [16], and we refer the reader to [5,26] for more references. In contrast to the number of papers available for the case when m(x) = m is a constant and µ 1 = µ 2 and for the case when the domain Ω does not change over time, much less is known when m(x) is a nonnegative function and µ 1 = µ 2 for problem (1).…”

Section: Huiling LI Xiaoliu Wang and Xueyan Lumentioning

confidence: 99%

A nonlinear Stefan problem with variable exponent and different moving parameters

Li¹,

Wang²,

Lu³

2020

Discrete &Amp; Continuous Dynamical Systems - B

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In this paper, we consider a nonlinear diffusion problem with variable exponent, accompanied by double free boundaries possessing different moving parameters, where the variable exponent function m(x) satisfies that m(x) − 1 can change its sign. Local existence and uniqueness of solution are established firstly, and then, some sufficient conditions are achieved for finite time blowup, and as well for global existence. Asymptotic behavior is further investigated for global solution, and existences of fast solution and slow solution are presented by making use of upper-sub solutions, energy and scaling arguments.

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