Blow-up for degenerate nonlinear parabolic problem

In this paper, we deal with the existence, uniqueness, and finite time blow-up of the solution to the degenerate nonlinear parabolic problem: uτ=(ξrumuξ)ξ/ξr + up for 0 < ξ < a, 0 < τ < Γ, u (ξ, 0) = u0 (ξ) for 0 ≤ ξ ≤ a, and u (0, τ) = 0 = u (a, τ) for 0 < τ < Γ, where u0 (ξ) is a...

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Bibliographic Details
Published inAIMS mathematics Vol. 4; no. 5; pp. 1488 - 1498
Main Author Y. Chan, W.
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2019
Subjects
blow-up
degenerate nonlinear parabolic problem
global existence
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Summary:In this paper, we deal with the existence, uniqueness, and finite time blow-up of the solution to the degenerate nonlinear parabolic problem: uτ=(ξrumuξ)ξ/ξr + up for 0 < ξ < a, 0 < τ < Γ, u (ξ, 0) = u0 (ξ) for 0 ≤ ξ ≤ a, and u (0, τ) = 0 = u (a, τ) for 0 < τ < Γ, where u0 (ξ) is a positive function and u0 (0) = 0 = u0 (a). In addition, we prove that u exists globally if a is small through constructing a global-exist upper solution, and uτ blows up in a finite time.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2019.5.1488