TY - JOUR
T1 - Strong periodic solutions for a class of abstract evolution equations
AU - Łukaszewicz, G.
AU - Ortega-Torres, E. E.
AU - Rojas-Medar, M. A.
PY - 2003/9
Y1 - 2003/9
N2 - We study a class of abstract nonlinear evolution equations in a separable Hilbert space for which we prove existence of strong time periodic solutions, provided the right-hand side is periodic and C1 in time, and small enough in the norm of the considered space. We prove also uniqueness and stability of the solutions. The results apply, in particular, in several models of hydrodynamics, such as magneto-micropolar and micropolar models, and classical magnetohydrodynamics and Navier-Stokes models with non-homogeneous boundary conditions. The existence part of the proof is based on a set of estimates for the family of finite-dimensional approximate solutions.
AB - We study a class of abstract nonlinear evolution equations in a separable Hilbert space for which we prove existence of strong time periodic solutions, provided the right-hand side is periodic and C1 in time, and small enough in the norm of the considered space. We prove also uniqueness and stability of the solutions. The results apply, in particular, in several models of hydrodynamics, such as magneto-micropolar and micropolar models, and classical magnetohydrodynamics and Navier-Stokes models with non-homogeneous boundary conditions. The existence part of the proof is based on a set of estimates for the family of finite-dimensional approximate solutions.
KW - Existence
KW - Galerkin approximation
KW - Hydrodynamics
KW - Periodic solution
KW - Stability
KW - Uniqueness
UR - https://www.scopus.com/pages/publications/0038112070
U2 - 10.1016/S0362-546X(03)00125-1
DO - 10.1016/S0362-546X(03)00125-1
M3 - Article
AN - SCOPUS:0038112070
SN - 0362-546X
VL - 54
SP - 1045
EP - 1056
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
IS - 6
ER -