Global existence for quasilinear diffusion equations in isotropic nondivergence form
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Volume 9 (2010) no. 3, p. 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
@article{ASNSP_2010_5_9_3_523_0,
     author = {Arendt, Wolfgang and Chill, Ralph},
     title = {Global existence for quasilinear diffusion equations in isotropic nondivergence form},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 9},
     number = {3},
     year = {2010},
     pages = {523-539},
     zbl = {1223.35202},
     mrnumber = {2722654},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2010_5_9_3_523_0}
}
Arendt, Wolfgang; Chill, Ralph. Global existence for quasilinear diffusion equations in isotropic nondivergence form. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Volume 9 (2010) no. 3, pp. 523-539. http://www.numdam.org/item/ASNSP_2010_5_9_3_523_0/

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