2020
DOI: 10.3934/era.2020005
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Initial boundary value problem for a inhomogeneous pseudo-parabolic equation

Abstract: This paper deals with the global existence and blow-up of solutions to a inhomogeneous pseudo-parabolic equation with initial value u 0 in the Sobolev space H 1 0 (Ω), where Ω ⊂ R n (n ≥ 1 is an integer) is a bounded domain. By using the mountain-pass level d (see (14)), the energy functional J (see (12)) and Nehari function I (see (13)), we decompose the space H 1 0 (Ω) into five parts, and in each part, we show the solutions exist globally or blow up in finite time. Furthermore, we study the decay rates for … Show more

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Cited by 12 publications
(9 citation statements)
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“…We also refer to the recent papers [36,44,12,31,33,60,62,37,41,21,6] for the study of asymptotic behavior of semilinear pseudo-parabolic equations. If α = 1, m > 0, and 0 < σ = 1, Ji et al [29] considered the Cauchy problem of the following fractional pseudo-parabolic equation u t − m∆u t + (−∆) σ u = u p+1 , p > 0.…”
Section: 2mentioning
confidence: 99%
“…We also refer to the recent papers [36,44,12,31,33,60,62,37,41,21,6] for the study of asymptotic behavior of semilinear pseudo-parabolic equations. If α = 1, m > 0, and 0 < σ = 1, Ji et al [29] considered the Cauchy problem of the following fractional pseudo-parabolic equation u t − m∆u t + (−∆) σ u = u p+1 , p > 0.…”
Section: 2mentioning
confidence: 99%
“…To be a little more precise, when ω0 and μ>ωλ1, the local well‐posedness, global existence, and finite time blow‐up of solutions were studied in Ref. 2, 9 by using potential well theory, which was firstly introduced by Sattinger and Payne 11,12 , then developed by Liu and Zhao 13 (see also the references 14–21 for this method). Moreover, the lower bound of the blow‐up time for blow‐up solutions was investigated in Refs.…”
Section: Introduction and Main Resultsmentioning
confidence: 99%
“…leading to global existence, and we can even confirm this by knowledge of parabolic equation [2,10,16,18,26,29,28,32,33], we have not been able to find an effective way to prove it. Up to now, this question is still open.…”
mentioning
confidence: 93%