Abstract and Applied Analysis

On the Blow-Up Set for Non-Newtonian Equation with a Nonlinear Boundary Condition

Zhilei Liang

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Abstract

We identify the blow-up set of solutions to the problem u t = ( | u x | p - 2 u x ) x , x > 0 , t ( 0 , T ) , - | u x | p - 2 u x ( 0 , t ) = u p - 1 ( 0 , t ) , t ( 0 , T ) , and u ( x , 0 ) = u 0 ( x ) 0 , x > 0 , where p > 2 . We obtain that the blow up set B ( u ) satisfies [ 0 , p ( p - 1 ) / ( p - 2 ) ) B ( u ) [ 0 , p ( p - 1 ) / ( p - 2 ) ] . The proof is based on the analysis of the asymptotic behavior of self-similar representation and on the comparison methods.

Article information

Source
Abstr. Appl. Anal., Volume 2010 (2010), Article ID 680572, 12 pages.

Dates
First available in Project Euclid: 1 November 2010

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1288620777

Digital Object Identifier
doi:10.1155/2010/680572

Mathematical Reviews number (MathSciNet)
MR2726611

Zentralblatt MATH identifier
1207.35247

Citation

Liang, Zhilei. On the Blow-Up Set for Non-Newtonian Equation with a Nonlinear Boundary Condition. Abstr. Appl. Anal. 2010 (2010), Article ID 680572, 12 pages. doi:10.1155/2010/680572. https://projecteuclid.org/euclid.aaa/1288620777


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