Space-Time Estimates of Mild Solutions of a Class of Higher-Order Semilinear Parabolic Equations in L p

Albert N. Sandjo ; Célestin Wafo Soh

Nonautonomous Dynamical Systems, Tome 1 (2014), / Harvested from The Polish Digital Mathematics Library

Résumé

We establish the well-posedness of boundary value problems for a family of nonlinear higherorder parabolic equations which comprises some models of epitaxial growth and thin film theory. In order to achieve this result, we provide a unified framework for constructing local mild solutions in C0([0, T]; Lp(Ω)) by introducing appropriate time-weighted Lebesgue norms inspired by a priori estimates of solutions. This framework allows us to obtain global existence of solutions under the proviso that initial data are reasonably small

Détail

Publié le : 2014-01-01

Zbl 1288.35009

EUDML-ID : urn:eudml:doc:267445

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