A global continuation theorem for obtaining eigenvalues and bifurcation points
Let be a closed set of , whose conormai cones , , have locally empty intersection. We first show in §1 that , is a function. We then represent the n microfunctions of , , using cohomology groups of of degree 1. By the results of § 1-3, we are able to prove in §4 that the sections of , , satisfy the principle of the analytic continuation in the complex integral manifolds of , being a base for the linear hull of in ; in particular we get . When is a half space with -boundary,...
If is a polynomial in such that integrable, then the inverse Fourier transform of is a fundamental solution to the differential operator . The purpose of the article is to study the dependence of this fundamental solution on the polynomial . For it is shown that can be analytically continued to a Riemann space over the set of all polynomials of the same degree as . The singularities of this extension are studied.
We consider a linear model of interaction between a viscous incompressible fluid and a thin elastic structure located on a part of the fluid domain boundary, the other part being rigid. After having given an existence and uniqueness result for the direct problem, we study the question of approximate controllability for this system when the control acts as a normal force applied to the structure. The case of an analytic boundary has been studied by Lions and Zuazua in [9] where, in particular,...