BOUNDARY STABILIZATION OF DONNELLS SHALLOW CIRCULAR CYLINDRICAL-SHELL

Donnell's model of a shallow (and thin) circular cylindrical shell is formulated by a system of three partial differential equations, only o ne elf which contains explicit time dependence. It constitutes one of the most important linear shell models, yet problems associated with i ts boundary stabilization and control have not been carefully studied. In this paper, we set up the functional-analytic framework, derive di ssipative boundary conditions, and determine the infinitesimal generat or of the semigroup of evolution. Using a frequency domain method alon g with ene-gy multipliers, we establish the result of uniform exponent ial decay of energy under geometric conditions identical to those of t he case of a thin Kirchhoff plate. Our approach, incorporating energy multipliers in the frequency domain with a contrapositive argument, ap pears to be new. It has the beneficial effect of avoiding the necessit y to estimate lower order terms when the shell radius is not large. We also consider the case in which the domains contain angular corners; special treatment is required to handle the additional energy contribu ted by the twisting moments at corner points. Under the assumption of sufficient regularity, uniform exponential decay of energy is also est ablished for such domains. (C) 1998 Academic Press Limited.