In this paper we established the Carleman estimate for the two dimensional Lamé system with the zero Dirichlet boundary conditions. Using this estimate we proved the exact controllability result for the Lamé system with with a control locally distributed over a subdomain which satisfies to a certain type of nontrapping conditions.

We present conjectured exact expressions for two types of correlations in the dense O(n = 1) loop model on L×∞ square lattices with periodic boundary conditions. These are the probability that a point is surrounded by m loops and the probability that k consecutive points on a row are on the same or on different loops. The dense O(n = 1) loop model is equivalent to the bond percolation model at ...

We implement the new transform method for solving boundary value problems developed by Fokas for periodic boundary conditions. The approach presented here is not a replacement for classical methods nor is it necessarily an improvement. However, in addition to establishing that periodic problems can indeed be solve by the new transform method (which enhances further its scope and applicability),...

In this paper, we establish a new Lyapunov-type inequality for quasilinear systems with the anti-periodic boundary conditions. It improves some result of Wang [17]. As an application, we also obtain lower bounds for the eigenvalues of corresponding systems.

In this paper we present sufficient conditions for the existence of solutions to the periodic fourth order boundary value problem u(x) = f(x, u(x), u′(x), u′′(x), u′′′(x)) u(a) = u(b), i = 0, 1, 2, 3, for x ∈ [a, b], and f : [a, b] × R4 → R a continuous function. To the best of our knowledge it is the first time where this type of general nonlinearities is considered in fourth order equations w...

Consider a unidimensional, single-phase nonlinear Stefan problem with nonlinear source and permeance terms, and a Dirichlet boundary condition depending on the free-boundary function. This problem is important in groundwater ow. By immobilizing the free-boundary with the help of a Landau type transformation, together with a homogeneous transformation dealing with the nonhomogeneous Dirichlet bo...

We provide a reciprocal relation linking the effective conductivity of a composite with highly conducting phase interfaces to that of a composite with the same phase geometry but with an electrical contact resistance at phase interfaces. A field relationship linking the electric field inside a composite with highly conducting phase interfaces to the current in a composite with contact resistanc...

In this talk we address the issue of existence of weak solutions for the non-homogeneous Navier-Stokes system with Navier friction boundary conditions allowing the presence of vacuum zones and assuming rough conditions on the data. We also study the convergence, as the viscosity goes to zero, of weak solutions for the non-homogeneous Navier-Stokes system with Navier friction boundary conditions...

We consider an arbitrary translationally invariant chain model, with nearest neighbors interaction and satisfying periodic boundary condition. The approach developed here allows a thermodynamic description of the chain model directly in terms of grand potential per site. This thermodynamic function is derived from an auxiliary function constructed only from open connected sub-chains. To exempli...

We consider a stochastic optimal control problem for an heat equation with boundary noise and boundary controls. Under suitable assumptions on the coefficients, we prove existence of optimal controls in strong sense by solving the stochastic hamiltonian system related.