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

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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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  • 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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