| Abstract: | For the equations of the motion of Kelvin-Voight fluids (0.1) and for the semilinear abstract differential Eqs. (0.11)–(0.17)
arising in the theory of Sobolev equations (to which Eqs. (0.1) also belong), we study the four following nonlocal problems:
1) the solvability of the initial boundary problem for Eqs. (0.1) and the Cauchy problem for Eqs. (0.11)–(0.17) on the semiaxis
0<t≤∞; 2) the existence of periodic solutions of Eqs. (0.1) and Eqs. (0.11)–(0.17) with a free term periodic in t; 3) exponential
stability theory for solutions of Eqs. (0.1) and Eqs. (0.11)–(0.17) as t→∞ and related problems; 4) attractor theory for Eqs.
(0.1). Bibliography: 40 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 197, pp. 120–158, 1992. |
