UNIFORM BOUNDARY STABILIZATION OF THERMOELASTIC PLATES J. E. Lagncse Department of Mathematics Georgetown University Washington, DC 20057 USA 1. OIUEN'fA1.'ION Let n be a bounded, open, connected set in R2 having a Lipschitz boundary r. We assume that r = foufl where ro and r l are relatively open, disjoint subsets of r with rl f. 0. We denote by II = (111,112) the unit normal vector to r (when it exists) pointing out of n, and set T = (-V:!,III), a unit positively oriented tangent vector to r. Let T > 0, and set Q = nx(O,T), E = r,,(O,T), Eo = rox(O,T), EI = rlx(O,T). We consider the following boundary value problem which describes the small vibrations of a thin, homogeneous, isotropic, thermoelastic plate of uniform thickness h: ! PhW U + + = fa, {), - - + /&(1 + = Xo p + T2 - TI) iII Q, Ow w = Tv = 0 on Eo, ! + (l-p)BIW + It l ' !?J = - M T , + + = on EJ, all - Oii =- >d D- {) 011 E, where' = {}f at and where {)2w _.2 {}2w _2 ()2w B1w = 2111112 7JXOy - VI ayr - "2 IJX1"' _,) _2 {}2w {)2w a 2 w B2W = (VI - "2)7JXOy + 1I 1112 (ayr - IJX1"). In the above system, w denotes vertical deflection of the plate and {) the deviation of the temperature from a reference temperature at which the plate is free of thermal stress. The various parameters which appear have the following meanings: p: mass density; D: flexural rigidity; p: Poisson's ratio; fa: vertical loading on the faces of the plate;