Non-simultaneous blow-up of n components for nonlinear parabolic systems

Liu, Bingchen; Li, Fengjie

doi:10.1016/j.jmaa.2009.03.018

Cited by 5 publications

(5 citation statements)

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“…k 1 = k 2 = 0. It is interesting that the positions of u i 1 and u i 2 are arbitrary due to the different values of i 1 and i 2 , which is just the results in Theorem 3.1 of [1]. (ii) for k 1 = 0 and k 2 = 0 (or k 1 = 0 and k 2 = 0), u i 1 and u i 2 can blow up by themselves and only u i 1 (or u i 2 ) can provide sufficient help to the blow-up of u j ,…”

Section: Introduction and Main Resultsmentioning

confidence: 95%

“…In the previous paper [1], blow-up phenomena of n components are studied for the following parabolic system:…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

“…It can be checked from Rossi [7] that the positive solution of (1 Introduce some notations, defined in [1], as follows,…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

“…By Green's identity,ū n ≤ M n . Thenū n satisfies that In fact, the proof of Lemma 3.3 is similar to the Lemma 3.3 in [1]. We omit the detail here.…”

Section: F LI and B Liumentioning

confidence: 86%

“…In fact, the proof can be obtained by using the similar method used in Lemma 3.5 of [1]. So we omit the detail here.…”

Section: F LI and B Liumentioning

confidence: 99%

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Note on nonsimultaneous blow-up ofncomponents for nonlinear parabolic systems

Liu

2014

Applicable Analysis

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This paper deals with the nonsimultaneous blow-up problems forThe main results extend the existence of two components blowing up simultaneously in the paper J. Math. Anal. Appl. 2009;356:215-231 to the case of k(∈ {2, 3, . . . , n − 1}) components blowing up simultaneously. We verify that blowup phenomena are independent of the choosing of the initial data in some exponent regions, while, in some others, the blow-up phenomena depend sensitively on the choosing of initial data. Moreover, the blow-up rates and sets are obtained for blow-up components.

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Section: Introduction and Main Resultsmentioning

confidence: 95%

“…In the previous paper [1], blow-up phenomena of n components are studied for the following parabolic system:…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

“…It can be checked from Rossi [7] that the positive solution of (1 Introduce some notations, defined in [1], as follows,…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

“…By Green's identity,ū n ≤ M n . Thenū n satisfies that In fact, the proof of Lemma 3.3 is similar to the Lemma 3.3 in [1]. We omit the detail here.…”

Section: F LI and B Liumentioning

confidence: 86%

“…In fact, the proof can be obtained by using the similar method used in Lemma 3.5 of [1]. So we omit the detail here.…”

Section: F LI and B Liumentioning

confidence: 99%

See 3 more Smart Citations