# 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

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topAlbert 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 -

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