Cauchy problem for semilinear parabolic equations with initial data in Hps(Rn) spaces.

Ribaud, Francis. "Cauchy problem for semilinear parabolic equations with initial data in Hps(Rn) spaces.." Revista Matemática Iberoamericana 14.1 (1998): 1-46. <http://eudml.org/doc/39552>.

@article{Ribaud1998,
abstract = {We study local and global Cauchy problems for the Semilinear Parabolic Equations ∂tU - ΔU = P(D) F(U) with initial data in fractional Sobolev spaces Hps(Rn). In most of the studies on this subject, the initial data U0(x) belongs to Lebesgue spaces Lp(Rn) or to supercritical fractional Sobolev spaces Hps(Rn) (s &gt; n/p). Our purpose is to study the intermediate cases (namely for 0 &lt; s &lt; n/p). We give some mapping properties for functions with polynomial growth on subcritical Hps(Rn) spaces and we show how to use them to solve the local Cauchy problem for data with low regularity. We also give some results about the global Cauchy problem for small initial data.},
author = {Ribaud, Francis},
journal = {Revista Matemática Iberoamericana},
keywords = {Problema de Cauchy; Ecuaciones parabólicas; Espacios de Sobolev; Valores iniciales; subcritical fractional Sobolev spaces; small initial data; initial data with low regularity; local and global Cauchy problems; polynomial growth},
language = {eng},
number = {1},
pages = {1-46},
title = {Cauchy problem for semilinear parabolic equations with initial data in Hps(Rn) spaces.},
url = {http://eudml.org/doc/39552},
volume = {14},
year = {1998},
}

TY - JOUR
AU - Ribaud, Francis
TI - Cauchy problem for semilinear parabolic equations with initial data in Hps(Rn) spaces.
JO - Revista Matemática Iberoamericana
PY - 1998
VL - 14
IS - 1
SP - 1
EP - 46
AB - We study local and global Cauchy problems for the Semilinear Parabolic Equations ∂tU - ΔU = P(D) F(U) with initial data in fractional Sobolev spaces Hps(Rn). In most of the studies on this subject, the initial data U0(x) belongs to Lebesgue spaces Lp(Rn) or to supercritical fractional Sobolev spaces Hps(Rn) (s &gt; n/p). Our purpose is to study the intermediate cases (namely for 0 &lt; s &lt; n/p). We give some mapping properties for functions with polynomial growth on subcritical Hps(Rn) spaces and we show how to use them to solve the local Cauchy problem for data with low regularity. We also give some results about the global Cauchy problem for small initial data.
LA - eng
KW - Problema de Cauchy; Ecuaciones parabólicas; Espacios de Sobolev; Valores iniciales; subcritical fractional Sobolev spaces; small initial data; initial data with low regularity; local and global Cauchy problems; polynomial growth
UR - http://eudml.org/doc/39552
ER -