Global existence for quasilinear diffusion equations in isotropic nondivergence form
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 9 (2010) no. 3, pp. 523-539.

We consider the quasilinear parabolic equation u t - β ( t , x , u , u ) Δ u = f ( t , x , u , u ) in a cylindrical domain, together with initial-boundary conditions, where the quasilinearity operates on the diffusion coefficient of the Laplacian. Under suitable conditions we prove global existence of a solution in the energy space. Our proof depends on maximal regularity of a nonautonomous linear parabolic equation which we use to provide us with compactness in order to apply Schaefer’s fixed point theorem.

Classification: 35K15,  35A05,  35K55
Arendt, Wolfgang 1; Chill, Ralph 2

1 Institut für Angewandte Analysis, Universität Ulm, D-89069 Ulm, Germany
2 Université Paul Verlaine - Metz, Laboratoire de Mathématiques et Applications de Metz et CNRS, UMR 7122, Bât. A, Ile du Saulcy, 57045 Metz Cedex 1, France
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Arendt, Wolfgang; Chill, Ralph. Global existence for quasilinear diffusion equations in isotropic nondivergence form. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 9 (2010) no. 3, pp. 523-539. http://archive.numdam.org/item/ASNSP_2010_5_9_3_523_0/

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