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

Albert N. Sandjo; Célestin Wafo Soh

Nonautonomous Dynamical Systems (2014)

  • Volume: 1, Issue: 1, page 83-92, electronic only
  • ISSN: 2353-0626

Abstract

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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

How to cite

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Albert N. Sandjo, and Célestin Wafo Soh. " Space-Time Estimates of Mild Solutions of a Class of Higher-Order Semilinear Parabolic Equations in L p ." Nonautonomous Dynamical Systems 1.1 (2014): 83-92, electronic only. <http://eudml.org/doc/267445>.

@article{AlbertN2014,
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},
author = {Albert N. Sandjo, Célestin Wafo Soh},
journal = {Nonautonomous Dynamical Systems},
keywords = {Epitaxy; Thin-film Equation; Scaling invariance; Lp − Lq Estimates; Analytic Semigroup; Kato’s Method; Mild Solution; epitaxy; thin-film equation; scaling invariance; estimates; analytic semigroup; Kato's method; mild solution},
language = {eng},
number = {1},
pages = {83-92, electronic only},
title = { Space-Time Estimates of Mild Solutions of a Class of Higher-Order Semilinear Parabolic Equations in L p },
url = {http://eudml.org/doc/267445},
volume = {1},
year = {2014},
}

TY - JOUR
AU - Albert N. Sandjo
AU - Célestin Wafo Soh
TI - Space-Time Estimates of Mild Solutions of a Class of Higher-Order Semilinear Parabolic Equations in L p
JO - Nonautonomous Dynamical Systems
PY - 2014
VL - 1
IS - 1
SP - 83
EP - 92, electronic only
AB - 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
LA - eng
KW - Epitaxy; Thin-film Equation; Scaling invariance; Lp − Lq Estimates; Analytic Semigroup; Kato’s Method; Mild Solution; epitaxy; thin-film equation; scaling invariance; estimates; analytic semigroup; Kato's method; mild solution
UR - http://eudml.org/doc/267445
ER -

References

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