NULL BOUNDARY CONTROLLABILITY FOR A FOURTH ORDER SEMILINEAR EQUATION

Finite Dimensional Null Controllability for the Semilinear Heat Equation

ABSTRACI’. We study a finite dimensional version of the null controllability problem for semilinear heat equations in bounded domains R of R” with Dirichlet boundary conditions. The control acts on any open an non-empty subset of R. The question under consideration is the following: given an initial state, a control time t = 2’ and a finite dimensional subspace E of L”(n), is there a control su...

Local Boundary Controllability for the Semilinear Plate Equation

The problem of local controllability for the semilinear plate equation with Dirichlet boundary conditions is studied. By making use of Schauder’s fixed point theorem and the inverse function theorem, we prove that this system is locally controllable under a super-linear assumption on the nonlinearity, that is, the initial states in a small neighborhood of 0 in a certain function space can be dr...

Blow-Up in a Fourth-Order Semilinear Parabolic Equation From . . .

Boundary local null-controllability of the Kuramoto-Sivashinsky equation

We prove that the Kuramoto-Sivashinsky equation is locally controllable in 1D and in 2D with one boundary control. Our method consists in combining several general results in order to reduce the nullcontrollability of this nonlinear parabolic equation to the exact controllability of a linear beam or plate system. This improves known results on the controllability of Kuramoto-Sivashinsky equatio...

Null Controllability of the Semilinear Heat

This paper is concerned with the null controllability of sys tems governed by semilinear parabolic equations The control is exerted either on a small subdomain or on a portion of the boundary We prove that the system is null controllable when the nonlinear term f s grows slower than s log jsj as jsj Introduction Assume a bounded and connected open set R with regular bound ary a nonempty open su...