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Properties of non-simultaneous blow-up solutions in nonlocal parabolic equations

โœ Scribed by Bingchen Liu; Fengjie Li

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
596 KB
Volume
72
Category
Article
ISSN
0362-546X

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โœฆ Synopsis

This paper deals with blow-up solutions in parabolic equations coupled via nonlocal nonlinearities, subject to homogeneous Dirichlet conditions. Firstly, some criteria on nonsimultaneous and simultaneous blow-up are given, including four kinds of phenomena: (i) the existence of non-simultaneous blow-up; (ii) the coexistence of non-simultaneous and simultaneous blow-up; (iii) any blow-up must be simultaneous; (iv) any blow-up must be non-simultaneous. Next, total versus single point blow-up are classified completely. Moreover, blow-up rates are obtained for both non-simultaneous and simultaneous blowup solutions.

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