Abstract
This is an article to introduce discrete nonlinear p-Laplacian parabolic equations on networks and discuss the conditions under which blow-up occurs for the solutions. We first deal with the case p = 2, introducing a recent result about the blow-up phenomena for the solutions. Secondly, we deal with the general p-Laplacian case. In each case, we classify the parameters depending on the equations so that we can see when the solutions blow up or globally exist. Moreover, the blow-up time and blow-up rate are introduced for the blow-up solutions. The last part is devoted to the blow-up of Fujita type.
This work is dedicated to Prof. Stevan Pilipovic for his 65th birthday
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Chung, SY. (2017). Blow-up Phenomena for Solutions of Discrete Nonlinear p-Laplacian Parabolic Equations on Networks. In: Oberguggenberger, M., Toft, J., Vindas, J., Wahlberg, P. (eds) Generalized Functions and Fourier Analysis. Operator Theory: Advances and Applications(), vol 260. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-51911-1_4
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DOI: https://doi.org/10.1007/978-3-319-51911-1_4
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-51910-4
Online ISBN: 978-3-319-51911-1
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