Abstract and Applied Analysis

Blow-Up Analysis for a Quasilinear Parabolic Equation with Inner Absorption and Nonlinear Neumann Boundary Condition

Abstract

We investigate an initial-boundary value problem for a quasilinear parabolic equation with inner absorption and nonlinear Neumann boundary condition. We establish, respectively, the conditions on nonlinearity to guarantee that $u(x,t)$ exists globally or blows up at some finite time ${t}^{\ast}$. Moreover, an upper bound for ${t}^{\ast}$ is derived. Under somewhat more restrictive conditions, a lower bound for ${t}^{\ast}$ is also obtained.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 289245, 8 pages.

Dates
First available in Project Euclid: 6 October 2014

https://projecteuclid.org/euclid.aaa/1412607222

Digital Object Identifier
doi:10.1155/2014/289245

Mathematical Reviews number (MathSciNet)
MR3206777

Zentralblatt MATH identifier
07022099

Citation

Fang, Zhong Bo; Chai, Yan. Blow-Up Analysis for a Quasilinear Parabolic Equation with Inner Absorption and Nonlinear Neumann Boundary Condition. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 289245, 8 pages. doi:10.1155/2014/289245. https://projecteuclid.org/euclid.aaa/1412607222

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