Local and global solutions of well-posed integrated Cauchy problems

Pedro J. Miana. "Local and global solutions of well-posed integrated Cauchy problems." Studia Mathematica 187.3 (2008): 219-232. <http://eudml.org/doc/286353>.

@article{PedroJ2008,
abstract = {We study the local well-posed integrated Cauchy problem $v^\{\prime \}(t) = Av(t) + (t^\{α\})/Γ(α+1)x$, v(0) = 0, t ∈ [0,κ), with κ > 0, α ≥ 0, and x ∈ X, where X is a Banach space and A a closed operator on X. We extend solutions increasing the regularity in α. The global case (κ = ∞) is also treated in detail. Growth of solutions is given in both cases.},
author = {Pedro J. Miana},
journal = {Studia Mathematica},
keywords = {abstract Cauchy problems; integrated semigroups; distribution semigroups},
language = {eng},
number = {3},
pages = {219-232},
title = {Local and global solutions of well-posed integrated Cauchy problems},
url = {http://eudml.org/doc/286353},
volume = {187},
year = {2008},
}

TY - JOUR
AU - Pedro J. Miana
TI - Local and global solutions of well-posed integrated Cauchy problems
JO - Studia Mathematica
PY - 2008
VL - 187
IS - 3
SP - 219
EP - 232
AB - We study the local well-posed integrated Cauchy problem $v^{\prime }(t) = Av(t) + (t^{α})/Γ(α+1)x$, v(0) = 0, t ∈ [0,κ), with κ > 0, α ≥ 0, and x ∈ X, where X is a Banach space and A a closed operator on X. We extend solutions increasing the regularity in α. The global case (κ = ∞) is also treated in detail. Growth of solutions is given in both cases.
LA - eng
KW - abstract Cauchy problems; integrated semigroups; distribution semigroups
UR - http://eudml.org/doc/286353
ER -