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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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Sandjo A. N., Soh C. W.

Nonautonomous Dynamical Systems

2014

tom 1

nr 1

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

Ograniczanie wyników

1 Nonautonomous Dynamical Systems

1 Sandjo A. N.

1 Soh C. W.

1 2014

Wyniki wyszukiwania

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