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Article . 2022 . Peer-reviewed
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AIMS Mathematics
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Non-Lipschitz heterogeneous reaction with a p-Laplacian operator

Authors: Díaz Palencia, José Luis;

Non-Lipschitz heterogeneous reaction with a p-Laplacian operator

Abstract

<abstract><p>The intention along this work is to provide analytical approaches for a degenerate parabolic equation formulated with a p-Laplacian operator and heterogeneous non-Lipschitz reaction. Firstly, some results are discussed and presented in relation with uniqueness, existence and regularity of solutions. Due to the degenerate diffusivity induced by the p-Laplacian operator (specially when $ \nabla u = 0 $, or close zero), solutions are studied in a weak sense upon definition of an appropriate test function. The p-Laplacian operator is positive for positive solutions. This positivity condition is employed to show the regularity results along propagation. Afterwards, profiles of solutions are explored specially to characterize the propagating front that exhibits the property known as finite propagation speed. Finally, conditions are shown to the loss of compact support and, hence, to the existence of blow up phenomena in finite time.</p></abstract>

Country
Spain
Keywords

critical exponent, Blow-up, Non-Lipschitz, P-Laplace, Critical exponent, p-laplace, non-lipschitz, heterogeneous reaction, QA1-939, Degenerate diffusion, Heterogeneous reaction, degenerate diffusion, blow-up, Mathematics

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
6
Top 10%
Average
Top 10%
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gold