Department of Mathematical Analysis, Faculty of Natural Sciences, Hongduc University, Thanh Hoa, Vietnam
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.
Le, A. (2020). Admissible inertial manifolds for second order in time evolution equations. Khayyam Journal of Mathematics, 6(2), 155-173. doi: 10.22034/kjm.2020.109813
MLA
Anh Minh Le. "Admissible inertial manifolds for second order in time evolution equations". Khayyam Journal of Mathematics, 6, 2, 2020, 155-173. doi: 10.22034/kjm.2020.109813
HARVARD
Le, A. (2020). 'Admissible inertial manifolds for second order in time evolution equations', Khayyam Journal of Mathematics, 6(2), pp. 155-173. doi: 10.22034/kjm.2020.109813
VANCOUVER
Le, A. Admissible inertial manifolds for second order in time evolution equations. Khayyam Journal of Mathematics, 2020; 6(2): 155-173. doi: 10.22034/kjm.2020.109813