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Blow-up for degenerate nonlinear parabolic problem

Department of Mathematics, Texas A&M University-Texarkana, Texarkana, TX 75503

Special Issues: Initial and Boundary Value Problems for Differential Equations

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 ≤ ξa, 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.
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Keywords blow-up; degenerate nonlinear parabolic problem; global existence

Citation: W. Y. Chan. Blow-up for degenerate nonlinear parabolic problem. AIMS Mathematics, 2019, 4(5): 1488-1498. doi: 10.3934/math.2019.5.1488

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