in this paper, two inverse problems of stephen kind with local (dirichlet) boundary conditions are investigated. in the first problem only a part of boundary is unknown and in the second problem, the whole of boundary is unknown. for the both of problems, at first, analytic expressions for unknown boundary are presented, then by using these analytic expressions for unknown boundaries and bounda...

Periodic travelling waves are an important solution form in oscillatory reaction–diffusion equations. I have shown previously that such waves arise naturally near a boundary at which a Dirichlet condition is applied. This result has applications in ecology, providing a potential explanation for the periodic waves seen in a number of natural populations. However, in ecological applications the D...

In this paper, we study strong solutions to the steady compressible heat-conductive fluid near a non-zero constant flow with the Dirichlet boundary condition for the velocity on the inflow and outflow part of the boundary. We also consider the Dirichlet boundary condition for the temperature, and we do not need the thermal conductivity coefficient κ to be large. The existence of strong solution...

in this paper, we study the casimir effect of a scalar field with dirichlet boundary condition in some certain topologies. by numerical analysis we show that casimir energy is a shape-dependent quantity. we also obtain the phase transition in different topologies in which the casimir force changes from attractive to repulsive or vice versa.  eararqr

We give a new derivation of Robin boundary conditions and interface jump conditions for the diffusion equation in one dimension. To derive a Robin boundary condition, we consider the diffusion equation with a boundary condition that randomly switches between a Dirichlet and a Neumann condition. We prove that, in the limit of infinitely fast switching rate with the proportion of time spent in th...

in this paper we provide‎ ‎existence results for positive solution to‎ ‎dirichlet p(t)-laplacian boundary value problems‎. ‎the sublinear and‎ ‎superlinear cases are considerd‎.

Let Ω ⊂ Rd be a bounded domain with smooth boundary and let A ⊂⊂ Ω be a smooth, compactly embedded subdomain. Consider the operator − 1 2 ∆ in Ω − Ā with the Dirichlet boundary condition at ∂A and the Neumann boundary condition at ∂Ω, and let λ0(Ω, A) > 0 denote its principal eigenvalue. We discuss the question of monotonicity of λ0(Ω, A) in its dependence on the domain Ω. The main point of thi...

In this short note, we study the local well-posedness of a 3D model for incompressible Navier-Stokes equations with partical viscosity. This model was originally proposed by Hou-Lei in [4]. In a recent paper, we prove that this 3D model with partial viscosity will develop a finite time singularity for a class of initial condition using a mixed Dirichlet Robin boundary condition. The local well-...

We investigate the Wightman function, the bulk-to-boundary propagator, the mean field squared and the vacuum expectation values of energy-momentum tensor for a scalar field in AdS spacetime, in the presence of a brane perpendicular to the AdS boundary. On the brane the field operator obeys Robin boundary condition. The vacuum expectation values are decomposed into the boundary-free AdS and bran...