A Note on Aubin-Lions-Dubinskiĭ Lemmas
By Xiuqing Chen, A. Jungel, Jian‐Guo Liu. 2013
98 citations recorded by the source corpus.
Strong compactness results for families of functions in seminormed nonnegative cones in the spirit of the Aubin-Lions-Dubinskiĭ lemma are proven, refining some recent results in the literature. The first theorem sharpens slightly a result of Dubinskiĭ (in Mat. Sb. 67(109):609–642, 1965) for seminormed cones. The second theorem applies to piecewise constant functions in time and sharpens slightly the results of Dreher and Jüngel (in Nonlinear Anal. 75:3072–3077, 2012) and Chen and Liu (in Appl. Math. Lett. 25:2252–2257, 2012). An application is given, which is useful in the study of porous-medium or fast-diffusion type equations.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering
View Paper: https://www.semanticscholar.org/paper/625ebbb684a7b8c491cb592d0d402dc652aad5bd
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Citations in the corpus
- Global Existence Analysis of Cross-Diffusion Population Systems for Multiple Species (2016, background): “Then relative compactness follows from a nonlinear version of the Aubin-Lions theorem [5].”
- The boundedness-by-entropy principle for cross-diffusion systems (2014, unknown): “Using Lemma 5 in [18] and the bounds on (yτ ), (zτ ), the first integral can be estimated as J1 ≤ ‖y(2) τzτ‖L2(0,T ;H1(Ω))‖πkzτ − zτ‖L2(0,T−k;H1(Ω)′) ≤ Ckτ‖πτzτ − zτ‖L1(0,T−τ ;H1(Ω)′) ≤ Ck,”
- Some variants of the classical Aubin–Lions Lemma (2014, background): “Possible extensions to the case of discretized evolutions equations may be possible, as it was studied in [1, 5] for instance.”
- The boundedness-by-entropy method for cross-diffusion systems (2015, background): “Using lemma 5 in [19] and the bounds on (yτ ), (zτ ), the first integral can be estimated as J1 ‖y2 τ zτ‖L2(0,T ;H 1( ))‖πkzτ − zτ‖L2(0,T −k;H 1( )′) Ck1/2τ−1‖πτzτ − zτ‖L1(0,T −τ ;H 1( )′) Ck,”