We consider the Cauchy problem for an elliptic operator, formulated as a Nash game. The overspecified Cauchy data are split between two players: the first player solves the elliptic equation with the Dirichlet part of the Cauchy data prescribed over the accessible boundary and a variable Neumann condition (which we call first player’s strategy) prescribed over the inaccessible part of the bound...

In this thesis we study optimal boundary control problems in energy spaces, their construction of robust preconditioners and applications to arterial blood flow. More precisely we first consider the unconstrained optimal Dirichlet and Neumann boundary control problems for the Poisson equation as a model problem. In both cases it turns out that the control can be eliminated and thus a variationa...

I) We consider a system governed by a free boundary problem with Tresca condition on a part of the boundary of a material domain with a source term g through a parabolic variational inequality of the second kind. We prove the existence and uniqueness results to a family of distributed optimal control problems over g for each parameter h > 0, associated to the Newton law (Robin boundary conditio...

The boundary states for AdS 2 D-branes in Lorentzian AdS 3 space-time are presented. AdS 2 D-branes are algebraically defined by twisted Dirichlet boundary conditions and are located on twisted conjugacy classes of SL(2,R). Using free field representation of symmetry currents in the SL(2,R) WZNW model, the twisted Dirichlet gluing conditions among currents are translated to matching conditions ...

in this paper, we solve a inhomogeneous fractional klein-gordon equation by the method of separating variables. we apply the method for three boundary conditions, contain dirichlet, neumann, and robin boundary conditions, and solve some examples to illustrate the effectiveness of the method.

The boundary states for AdS 2 D-branes in Lorentzian AdS 3 space-time are presented. AdS 2 D-branes are algebraically defined by twisted Dirichlet boundary conditions and are located on twisted conjugacy classes of SL(2,R). Using free field representation of symmetry currents in the SL(2,R) WZNW model, the twisted Dirichlet gluing conditions among currents are translated to matching conditions ...

In this paper, we study Riesz basis property and stability for a nonuniform thermoelastic system with Dirichlet-Dirichlet boundary condition, where the heat subsystem is considered as control to whole coupled system. By means of matrix operator pencil method, obtain asymptotic expressions eigenpairs, which are exactly coincident constant coefficients case. We then show that there exists sequenc...

We consider a massless scalar field in 1+1 dimensions satisfying a Robin boundary condition (BC) at a non-relativistic moving boundary. We derive a Bogoliubov transformation between input and output bosonic field operators, which allows us to calculate the spectral distribution of created particles. The cases of Dirichlet and Neumann BC may be obtained from our result as limiting cases. These t...

In this paper, we aim to study the solutions of superlinear hyperbolic problems with boundary condition Dirichlet type where show existence and uniqueness strong for by method energy inequality.