Global existence for quasilinear diffusion equations in isotropic nondivergence form

Research output: Contribution to journalResearch articleContributedpeer-review


  • Wolfgang Arendt - , Ulm University (Author)
  • Ralph Chill - , Universite de Metz (Author)


We consider the quasilinear parabolic equation ut - β(t, x, u,δu)δu = f (t, x, u,δu) 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.


Original languageEnglish
Pages (from-to)523-539
JournalAnnali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V
Issue number3
Publication statusPublished - 2010
Externally publishedYes

External IDs

Scopus 83455201348
ORCID /0000-0002-6854-0586/work/142232387