In this article, we study stochastic partial differential equations with two reflecting walls h and h, driven by space-time white noise with non-constant diffusion coefficients under periodic boundary conditions. The existence and uniqueness of invariant measures is established under appropriate conditions. The strong Feller property is also obtained.

For any g > 2 we construct a graph Γg ⊂ S whose exteriorMg = S\N(Γg) supports a complete finite-volume hyperbolic structure with one toric cusp and a connected geodesic boundary of genus g. We compute the canonical decomposition and the isometry group of Mg, showing in particular that any selfhomeomorphism of Mg extends to a self-homeomorphism of the pair (S ,Γg), and that Γg is chiral. Buildin...

We describe a complete list of Casimirs for 2D Euler hydrodynamics on a surface without boundary: we define generalized enstrophies which, along with circulations, form a complete set of invariants for coadjoint orbits of area-preserving diffeomorphisms on a surface. We also outline a possible extension of main notions to the boundary case and formulate several open questions in that setting.

It is shown that certain natural maps between the ideal, Gromov, and end boundaries of a complete CAT(0) space can fail to be either injective or surjective. Additionally the natural map from the Gromov boundary to the end boundary of a complete CAT(−1) space can fail to be either injective or surjective.

in this paper, dynamic analysis of the composite truncated sandwich conical shells (stcs) with various boundary conditions subjected to low velocity impact was studied analytically, based on higher order sandwich panel theory. impact was assumed to occur normally over to the top face-sheet and the contact force history is predicted using two solution models of the motion are derived based on ha...

We consider a family of solutions to the evolutionary Navier-Stokes system supplemented with the complete slip boundary conditions on domains with rough boundaries. We give a complete description of the asymptotic limit by means of Γ−convergence arguments, and identify a general class of boundary conditions.

singular perturbation problems have been studied by many mathematicians. since the approximate solutions of these problems are as the sum of internal solution (boundary layer area) and external ones, the formation or non-formation of boundary layers should be specified. this paper, investigates this issue for a singular perturbation problem including a first order differential equation with gen...

In this paper we investigate vector-valued parabolic initial boundary value problems of relaxation type. Typical examples for such boundary conditions are dynamic boundary conditions or linearized free boundary value problems like in the Stefan problem. We present a complete Lp-theory for such problems which is based on maximal regularity of certain model problems.

the age of criminal responsibility of children in the islamic penalties act has been determined as religious bulugh (puberty) nasab. according to this, criminal authorities hold girls criminally liable and punishable at 9 complete lunar years and boys at 15 complete lunar years. unfortunately, our legislator has set criminal responsibility of children based on sexual maturity; therefore, thousa...