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         "type" : "Publication",
         "id"   : "https://puma.ub.uni-stuttgart.de/bibtex/26542ad7fbcea229e7f345790a76dbc7f/elkepeter",         
         "tags" : [
            "Lienstromberg","Analysis","IADM","PDEs","gradient-flow","FOS"
         ],
         
         "intraHash" : "6542ad7fbcea229e7f345790a76dbc7f",
         "interHash" : "939b1f264055663e904645113e2b2e05",
         "label" : "Non-Newtonian thin-film equations: global existence of solutions, gradient-flow structure and guaranteed lift-off",
         "user" : "elkepeter",
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         "date" : "2023-03-13 12:12:09",
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         "pub-type": "article",
         "publisher":"arXiv",
         "year": "2023", 
         "url": "https://arxiv.org/abs/2301.10300", 
         
         "author": [ 
            "Peter Gladbach","Jonas Jansen","Christina Lienstromberg"
         ],
         "authors": [
         	
            	{"first" : "Peter",	"last" : "Gladbach"},
            	{"first" : "Jonas",	"last" : "Jansen"},
            	{"first" : "Christina",	"last" : "Lienstromberg"}
         ],
         "abstract": "We study the gradient-flow structure of a non-Newtonian thin film equation with power-law rheology. The equation is quasilinear, of fourth order and doubly-degenerate parabolic. By adding a singular potential to the natural Dirichlet energy, we introduce a modified version of the thin-film equation. Then, we set up a minimising-movement scheme that converges to global positive weak solutions to the modified problem. These solutions satisfy an energy-dissipation equality and follow a gradient flow. In the limit of a vanishing singularity of the potential, we obtain global non-negative weak solutions to the power-law thin-film equation\r\n∂tu+∂x(m(u)|∂3xu−G\u2032\u2032(u)∂xu|α−1(∂3xu−G\u2032\u2032(u)∂xu))=0\r\nwith potential G in the shear-thinning (α>1), Newtonian (α=1) and shear-thickening case (0<α<1). The latter satisfy an energy-dissipation inequality. Finally, we derive dissipation bounds in the case G≡0 which imply that solutions emerging from initial values with low energy lift up uniformly in finite time.",
         "copyright" : "arXiv.org perpetual, non-exclusive license",
         
         "doi" : "10.48550/ARXIV.2301.10300",
         
         "bibtexKey": "https://doi.org/10.48550/arxiv.2301.10300"

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