Global existence and finite time blowup for a nonlocal semilinear pseudo-parabolic equation

In this paper, the initial boundary value problem for a nonlocal semilinear pseudo-parabolic equation is investigated, which was introduced to model phenomena in population dynamics and biological sciences where the total mass of a chemical or an organism is conserved. The existence, uniqueness and...

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Bibliographic Details
Published inAdvances in nonlinear analysis Vol. 10; no. 1; pp. 261 - 288
Main Authors Wang, Xingchang, Xu, Runzhang
Format Journal Article
LanguageEnglish
Published De Gruyter 01.01.2021
Subjects
35K10
35K20
nonlocal source
potential well
Semilinear parabolic equation
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Summary:In this paper, the initial boundary value problem for a nonlocal semilinear pseudo-parabolic equation is investigated, which was introduced to model phenomena in population dynamics and biological sciences where the total mass of a chemical or an organism is conserved. The existence, uniqueness and asymptotic behavior of the global solution and the blowup phenomena of solution with subcritical initial energy are established. Then these results are extended parallelly to the critical initial energy. Further the blowup phenomena of solution with supercritical initial energy is proved, but the existence, uniqueness and asymptotic behavior of the global solution with supercritical initial energy are still open.
ISSN:2191-9496
2191-950X
DOI:10.1515/anona-2020-0141