Extinction Phenomenon and Decay Estimate for a Quasilinear Parabolic Equation with a Nonlinear Source

Liu, Dengming; Yang, Lo

doi:10.1155/2021/5569043

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Introduction and Main Results1

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2021

2022

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Cited by 4 publications

(1 citation statement)

References 24 publications

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“…This means that the solutions corresponding to bounded non-negative initial data will vanish identically after a finite time. This was observed first by A. S. Kalashnikov in 1974 (see [16,17] and the references therein). Furthermore, for the case f (u) = c(x, t)u p , the authors of [18] discussed the parabolic equation with nonlinear nonlocal Neumann boundary conditions, in 2017.…”

Section: Introduction and Main Resultsmentioning

confidence: 65%

Analysis of Solutions to a Parabolic System with Absorption

Liu

2022

Symmetry

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In this paper, we investigate the blow-up rate and global existence of solutions to a parabolic system with absorption under the homogeneous Dirichlet boundary. By using the comparison principle and super-sub solution method, we obtain some sufficient conditions for the global existence and blow-up in finite time of solutions and establish some estimates of the upper and lower bounds of the blow-up rates. For the special case, if the domain is symmetric, for example, if it is a ball, the results of this paper also hold.

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Section: Introduction and Main Resultsmentioning

confidence: 65%