1993/12/31 by Ya. I. Alber, Alber, Ya. I.
Mathematics · #Differential Equations and Numerical Methods #Nonlinear Differential Equations Analysis #Differential Equations and Boundary Problems
paper · pdf · doi:10.48550/arxiv.funct-an/9312006
Known investigations of nonlinear evolution equations\n dx
over dt + A(t)x(t) = f(t)
,
quad x(t0) = x0,
quad t0
le t\nlt;
infty
,
eqno(0.1)\n with monotone operators A(t) acting from reflexive Banach space B to dual\nspace B^*, usually assume that along with B and B^* there is a Hilbert\nspace H and continuous imbedding B hookrightarrow H in the triplet\n B
hookrightarrow H
hookrightarrow B^*
;
eqno(0.2)\n and that B is dense in H. The stabilization of solutions of evolution\nequations has been proven either in the sense of weak convergence in B or in\nthe norm of H space, and only asymptotic estimates of stabilization rate have\nbeen obtained [15].\n In the present paper we consider equations of type (0.1) without conditions\n(0.2) and establish stabilization with both\n