NECESSARY AND SUFFICIENT CONDITIONS OF STABILIZATION OF SOLUTIONS OF THE FIRST BOUNDARY-VALUE PROBLEM FOR A PARABOLIC EQUATION

摘要

Necessary and sufficient conditions are established for the stabilization of the solution of the first boundary-value problem for a divergent second-order parabolic equation with no lower-order terms. For an arbitrary (possibly unbounded) domain Q ∈ R~N, N ≥ 3, with an initial function u_0(x) defined in Q for t = 0, one studies the influence of Q on the stabilization of the solution in the cylinder Z = Q x [0, ∞) with the homogeneous boundary conditions on the lateral surface of Z.