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Nonautonomous Dynamical Systems

formerly Nonautonomous and Stochastic Dynamical Systems

Editor-in-Chief: Diagana, Toka

Managing Editor: Cánovas, Jose

Mathematical Citation Quotient (MCQ) 2018: 0.62

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

Albert N. Sandjo / Célestin Wafo Soh
  • Department of Mathematics and Statistical Sciences, Jackson State University, JSU Box 17610, 1400 J R Lynch Str., Jackson, MS 39217, USA
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Published Online: 2014-05-17 | DOI: https://doi.org/10.2478/msds-2014-0003


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

Keywords : Epitaxy; Thin-film Equation; Scaling invariance; Lp − Lq Estimates; Analytic Semigroup; Kato’s Method; Mild Solution


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About the article

Received: 2014-01-16

Accepted: 2014-03-21

Published Online: 2014-05-17

Published in Print: 2014-01-01

Citation Information: Nonautonomous Dynamical Systems, Volume 1, Issue 1, ISSN (Online) 2353-0626, DOI: https://doi.org/10.2478/msds-2014-0003.

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© 2014 Albert N. Sandjo, Célestin Wafo Soh . This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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