Hyperbolic Equations in Uniform Spaces

J. W. Cholewa, and Tomasz Dlotko. "Hyperbolic Equations in Uniform Spaces." Bulletin of the Polish Academy of Sciences. Mathematics 52.3 (2004): 249-263. <http://eudml.org/doc/280998>.

@article{J2004,
abstract = {The paper is devoted to the Cauchy problem for a semilinear damped wave equation in the whole of ℝ ⁿ. Under suitable assumptions a bounded dissipative semigroup of global solutions is constructed in a locally uniform space $Ḣ¹_\{lu\}(ℝ ⁿ) × L̇²_\{lu\}(ℝ ⁿ)$. Asymptotic compactness of this semigroup and the existence of a global attractor are then shown.},
author = {J. W. Cholewa, Tomasz Dlotko},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {wave equation; uniform spaces; dissipativeness; global attractor; semilinear damped wave equation; bounded dissipative semigroup},
language = {eng},
number = {3},
pages = {249-263},
title = {Hyperbolic Equations in Uniform Spaces},
url = {http://eudml.org/doc/280998},
volume = {52},
year = {2004},
}

TY - JOUR
AU - J. W. Cholewa
AU - Tomasz Dlotko
TI - Hyperbolic Equations in Uniform Spaces
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2004
VL - 52
IS - 3
SP - 249
EP - 263
AB - The paper is devoted to the Cauchy problem for a semilinear damped wave equation in the whole of ℝ ⁿ. Under suitable assumptions a bounded dissipative semigroup of global solutions is constructed in a locally uniform space $Ḣ¹_{lu}(ℝ ⁿ) × L̇²_{lu}(ℝ ⁿ)$. Asymptotic compactness of this semigroup and the existence of a global attractor are then shown.
LA - eng
KW - wave equation; uniform spaces; dissipativeness; global attractor; semilinear damped wave equation; bounded dissipative semigroup
UR - http://eudml.org/doc/280998
ER -