A quasilinear parabolic problem with a source term and a nonlocal absorption

Li, Huiling; Wang, Heng-Ling; Wang, Xiao-Liu

doi:10.3934/cpaa.2018092

Cited by 2 publications

(3 citation statements)

References 26 publications

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“…In this paper, we continue the studies in [10] and provide a quite complete classification of the behavior of solutions to the problem (1.1).…”

Section: Introductionmentioning

confidence: 83%

“…We are interested in illustrating how this modification influences the dynamics of solutions. An exploring study in [10] shows that unlike the conclusion for the problem (1.3), the behavior of solutions to the problem (1.1) is not only influenced by the size of domain, but also impacted by positivity of the associated energy functional defined as…”

Section: Introductionmentioning

confidence: 93%

See 1 more Smart Citation

Global dynamics of a parabolic type equation arising from the curvature flow

Bai¹,

Li²,

Wang

2021

Preprint

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This paper studies a type of degenerate parabolic problem with nonlocal termwhere p > 1, a > 0. In this paper, the classification of the finite-time blowup/global existence phenomena based on the associated energy functional and explicit expression of all nonnegative steady states are demonstrated. Moreover, we combine the applications of Lojasiewicz-Simon inequality and energy estimates to derive that any bounded solution with positive initial data converges to some steady state as t → +∞.

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“…In this paper, we continue the studies in [10] and provide a quite complete classification of the behavior of solutions to the problem (1.1).…”

Section: Introductionmentioning

confidence: 83%

Section: Introductionmentioning

confidence: 93%

Global dynamics of a parabolic type equation arising from the curvature flow

Bai¹,

Li²,

Wang

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Therefore, from the viewpoint of mathematics, it is valuable and interesting to develop techniques to investigate problems without comparison principles and illustrate how this modification influences the dynamics of solutions. An exploring study in [7] shows that unlike the problem (1.2), the behavior of solutions to the problem (1.1) is not only influenced by the size of domain, but also impacted by positivity of the associated energy functional defined as…”

Section: Introductionmentioning

confidence: 99%