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

• Autorzy: Albert N. Sandjo , Célestin Wafo Soh
• Języki publikacji: EN

Abstrakty

EN

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

Słowa kluczowe

EN

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

• Wydawca: De Gruyter Open
• Czasopismo: Nonautonomous Dynamical Systems
• Rocznik: 2014
• Tom: 1
• Numer: 1

Daty

wydano

2014-01-01

otrzymano

2014-01-16

zaakceptowano

2014-03-21

online

2014-05-17

Twórcy

autor

Albert N. Sandjo

• RWTH Aachen University, Templergraben 55, 52056 Aachen, Germany

autor

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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Identyfikatory

DOI

10.2478/msds-2014-0003