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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access May 17, 2014

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

  • Albert N. Sandjo EMAIL logo and Célestin Wafo Soh

Abstract

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

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Received: 2014-1-16
Accepted: 2014-3-21
Published Online: 2014-5-17
Published in Print: 2014-1-1

© 2014 Albert N. Sandjo, Célestin Wafo Soh

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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