No abstract

No abstract

Abstract. Exponential decay is proven for a class of initial boundary value problems for the equation w u -CoWx~ = f (wt). The boundary condition is CoW x + rw t = 0 at x = 1 and w(0, t) = 0. Iffsatisfies a global Lipschitz condition, no restrictions are placed on the initial conditions, but if this is relaxed to a local Lipschitz condition, the initial data are assumed to be sufficiently small. These theorems are motivated in part by an application to modeling of "galloping" transmission lines. A theorem about boundedness of solutions without boundary damping is proven also. A global Lipschitz condition is assumed here, but the theorem is believed to be more generally true.

and are satisfied. M = sup {Il(iu-A)-'\\ I w E R)

Energy decay estimaks for a system of two hyperbolic equations coupled in series with boundary dissipation are studied. It is shown that under certain conditions in the joined surface of the two bounded domains of the equations in the space of R", the energy of the system will decay uniformly exponentially. J ( t ) =/u1[2m-Vu+(nl)u]dz+ 9[2m. Vu+("-1)uJdz. (2.3)Our goal is to prove existence of €0, a1,a2 such that (2.4) @ -E ( O, andrzS&@ 9 5 -a& for f 0. (2.5) Then, from (2.4) and (2.5) we obtain the desired result. In order to verify (2.4). first consider the Poincare's inequality with respect to each 01 91 -221 6/93/$3.00 (8 1993 IEEE