On uniform stabilization of the solution of the second mixed problem for a second order parabolic equation. (English. Russian original) Zbl 0645.35038

Gushchin, A. K.; Mikhajlov, V. P.; Mikhajlov, Yu. A.

Math. USSR, Sb. 56, 141-162 (1987); translation from Mat. Sb., Nov. Ser. 128(170), No. 2, 147-168 (1985).

On the line of earlier works of the first author, the paper is concerned with the uniform stabilization of the solution of the second mixed problem for a second order linear parabolic equation. The authors prove the stabilization criteria for large classes of unbounded domains including plane domains such as \[ \{(x_ 1,x_ 2): x_ 1>0,\quad | x_ 2| <kx\quad a_ 1,\quad k=const.>0,\quad a\in (0,1)\}. \] One also obtains estimates for the corresponding Green’s function.

Reviewer: S.Sburlan

MSC:

35K20	Initial-boundary value problems for second-order parabolic equations
35B40	Asymptotic behavior of solutions to PDEs

Keywords:

uniform stabilization; unbounded domains; Green’s function