We study an initial-boundary-value problem of a nonlinear Korteweg-de Vries equation posed on a finite interval (0, 2π). The whole system has Dirichlet boundary condition at the left end-point, and both of Dirichlet and Neumann homogeneous boundary conditions at the right end-point. It is known that the origin is not asymptotically stable for the linearized system around the origin. We prove th...

We consider a two-component competition-diffusion system with equal diffusion coefficients and inhomogeneous Dirichlet boundary conditions. When the interspecific competition parameter tends to infinity, the system solution converges to that of a freeboundary problem. If all stationary solutions of this limit problem are non-degenerate and if a certain linear combination of the boundary data do...

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 ...

As a model of the second order elliptic equation with non-trivial boundary conditions, we consider the Laplace equation with mixed Dirichlet and Neumann boundary conditions on convex polygonal domains. Our goal is to establish that finite element discrete harmonic functions with mixed Dirichlet and Neumann boundary conditions satisfy a weak (Agmon-Miranda) discrete maximum principle, and then p...

Immersed boundary methods are efficient tools of growing interest as they allow to use generic CFD codes to deal with complex, moving and deformable geometries, for a reasonable computational cost compared to classical bodyconformal or unstructured mesh approaches. In this work, we propose a new immersed boundary method based on a radial basis functions framework for the spreading-interpolation...

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 ...

We prove a well-posedness result for second order boundary value problems in weighted Sobolev spaces on curvilinear polyhedral domains in Rn with Dirichlet boundary conditions. Our typical weight is the distance to the set of singular boundary points.

The global solvability of the boundary value problem for stationarymagnetohydrodynamic equations under the Dirichlet boundary condition for the velocity and mixed boundary conditions for the magnetic field is proved. © 2014 Elsevier Ltd. All rights reserved.

Tension spline is a function that, for given partition x0 < x1 < . . . < xn, on each interval [xi, xi+1] satisfies differential equation (D − ρiD)u = 0, where ρi’s are prescribed nonnegative real numbers. In the literature, tension splines are used in collocation methods applied to two-points singularly perturbed boundary value problems with Dirichlet boundary conditions. In this paper, we adap...