Abstract
In this paper the conditions for the law of temperature behavior on a solid cylinder wall describes, under which the solution of a linear conjugate inverse initial-boundary value problem describing a two-layer axisymmetric creeping motion of viscous heat-conducting fluids tends to zero exponentially with increases of time
Highlights
Introduction and preliminariesIn work [1], the linear conjugate inverse initial boundary value problem describing a twolayer creeping motion of viscous heat-conducting fluids in a cylinder with a solid side surface r = R2 = const and interface r = h(t), 0 < h(t) < R2 was considered ( )v1t = ν1 v1rr + r v1r + f1(t), 0 < r < R1, (1)v2t = ν2 v2rr + r v2r + f2(t), R1 < r < R2, (2) ∫ R1 ∫ R2v1(R1, t) = v2(R1, t), rv1(r, t)dr + rv2(r, t)dr = 0, (3) R1
Note that M → 0 since the creeping motion considers in this paper
In paper [1] the priori estimates were obtained for the functions vj(r, t), aj(r, t), fj(t)
Summary
In work [1], the linear conjugate inverse initial boundary value problem describing a twolayer creeping motion of viscous heat-conducting fluids in a cylinder with a solid side surface r = R2 = const and interface r = h(t), 0 < h(t) < R2 was considered ( Victor K. Andreev, Evgeniy P. Magdenko On the Asymptotic Behavior of the Conjugate Problem . . . and the closed conjugate problem for functions aj(r, t) is described the following equations: ajt = χj ajrr + r ajr , a1(R1, t) = a2(R1, t), k1a1r(R1, t) = k2a2r(R2, t).
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