Uniform blow-up rates and asymptotic estimates of solutions for diffusion systems with nonlocal sources.
Cui, Zhoujin, Yang, Zuodong (2007)
Differential Equations & Nonlinear Mechanics
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Cui, Zhoujin, Yang, Zuodong (2007)
Differential Equations & Nonlinear Mechanics
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Chen, Botao, Mi, Yongsheng, Mu, Chunlai (2011)
Boundary Value Problems [electronic only]
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Liang, Zhilei (2010)
Abstract and Applied Analysis
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Fila, M., Filo, J.
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Youpeng Chen, Baozhu Zheng (2015)
Annales Polonici Mathematici
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This paper deals with the blow-up properties of positive solutions to a localized singular parabolic equation with weighted nonlocal nonlinear boundary conditions. Under certain conditions, criteria of global existence and finite time blow-up are established. Furthermore, when q=1, the global blow-up behavior and the uniform blow-up profile of the blow-up solution are described; we find that the blow-up set is the whole domain [0,a], including the boundary, in contrast to the case of...
Zhou, Jun, Mu, Chunlai, Li, Zhongping (2006)
Boundary Value Problems [electronic only]
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Rossi, J.D. (1998)
Acta Mathematica Universitatis Comenianae. New Series
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Cui, Zhoujin, Yang, Zuodong (2007)
International Journal of Mathematics and Mathematical Sciences
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Zhou, Jun (2007)
Surveys in Mathematics and its Applications
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Wang, Yulan, Mu, Chunlai, Xiang, Zhaoyin (2007)
Boundary Value Problems [electronic only]
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Juan Luis Vázquez (2004)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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We review the main mathematical questions posed in blow-up problems for reaction-diffusion equations and discuss results of the author and collaborators on the subjects of continuation of solutions after blow-up, existence of transient blow-up solutions (so-called peaking solutions) and avalanche formation as a mechanism of complete blow-up.