Geodesic
Nonuniqueness of solutions of initial-value problems for parabolic $p$-Laplacian
Electronic Journal of Differential Equations, Tome 2015 (2015).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We construct a positive solution to a quasilinear parabolic problem in a bounded spatial domain with the p-Laplacian and a nonsmooth reaction function. We obtain nonuniqueness for zero initial data. Our method is based on sub- and supersolutions and the weak comparison principle. Using the method of sub- and supersolutions we construct a positive solution to a quasilinear parabolic problem with the p-Laplacian and a reaction function that is non-Lipschitz on a part of the spatial domain. Thereby we obtain nonuniqueness for zero initial data.
Classification : 35B05, 35B30, 35K15, 35K55, 35K65
Keywords: quasilinear parabolic equations with p-Laplacian, nonuniqueness for initial-boundary value problem, sub- and supersolutions, comparison principle 
@article{EJDE_2015__2015__a32,
     author = {Benedikt, Jiri and Bobkov, Vladimir E. and Girg, Petr and Kotrla, Lukas and Takac, Peter},
     title = {Nonuniqueness of solutions of initial-value problems for parabolic $p${-Laplacian}},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2015},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a32/}
}
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%J Electronic Journal of Differential Equations
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Benedikt, Jiri; Bobkov, Vladimir E.; Girg, Petr; Kotrla, Lukas; Takac, Peter. Nonuniqueness of solutions of initial-value problems for parabolic $p$-Laplacian. Electronic Journal of Differential Equations, Tome 2015 (2015). http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a32/