We consider the quasilinear parabolic equation 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.
@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}, pages = {523--539}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 9}, number = {3}, year = {2010}, mrnumber = {2722654}, zbl = {1223.35202}, language = {en}, url = {http://archive.numdam.org/item/ASNSP_2010_5_9_3_523_0/} }
TY - JOUR AU - Arendt, Wolfgang AU - Chill, Ralph TI - Global existence for quasilinear diffusion equations in isotropic nondivergence form JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2010 SP - 523 EP - 539 VL - 9 IS - 3 PB - Scuola Normale Superiore, Pisa UR - http://archive.numdam.org/item/ASNSP_2010_5_9_3_523_0/ LA - en ID - ASNSP_2010_5_9_3_523_0 ER -
%0 Journal Article %A Arendt, Wolfgang %A Chill, Ralph %T Global existence for quasilinear diffusion equations in isotropic nondivergence form %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2010 %P 523-539 %V 9 %N 3 %I Scuola Normale Superiore, Pisa %U http://archive.numdam.org/item/ASNSP_2010_5_9_3_523_0/ %G en %F 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, 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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