Abstract :
We consider problems of the form
d2u
dt2
+ Au = F, αu(0) + u(T ) = g, β
du
dt
(0)+ du
dt
(T ) = h,
for t ∈ (0,T ), where A is a densely defined, linear, time independent, positive definite
symmetric operator and α and β are constants. Although most of our results would hold
for more general operators A, we restrict attention to the case in which A is a differential
operator and determine ranges of values of α and β for which it is possible to obtain energy
bounds, uniqueness results, and, in a special case, pointwise bounds. Some extensions
which include a damping term or a term which arises in a generalization of the Kirchhoff
string model are also discussed.
2002 Elsevier Science (USA). All rights reserved.
