@article {
author = {Le, Anh},
title = {Admissible inertial manifolds for second order in time evolution equations},
journal = {Khayyam Journal of Mathematics},
volume = {6},
number = {2},
pages = {155-173},
year = {2020},
publisher = {Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures)},
issn = {2423-4788},
eissn = {2423-4788},
doi = {10.22034/kjm.2020.109813},
abstract = {We prove the existence of admissible inertial manifolds for the second order in time evolution equations of the form $$ \ddot{x}+2\varepsilon \dot{x}+Ax=f(t,x)$$ when $A$ is positive definite and self-adjoint with a discrete spectrum and the nonlinear term $f$ satisfies the $\varphi$-Lipschitz condition, that is, $\|f(t,x)-f(t,y)\|\leqslant\varphi(t)\left \|A^{\beta}(x-y)\right \|$ for $\varphi$ belonging to one of the admissible Banach function spaces containing wide classes of function spaces like $L_{p}$-spaces, the Lorentz spaces $L_{p,q}$, and many other function spaces occurring in interpolation theory.},
keywords = {Admissible inertial manifolds,second order in time evolution equations,admissible function spaces,Lyapunov--Perron method},
url = {https://www.kjm-math.org/article_109813.html},
eprint = {https://www.kjm-math.org/article_109813_372333a09954785108dc346740036a94.pdf}
}