First, notions of inside components and outside components are introduced for any subset of n-dimensional Euclid space. Next, notions of the bounded domain and the unbounded domain are defined using the above components. If the dimension is larger than 1, and if a subset is bounded, a unbounded domain of the subset coincides with an outside component (which is unique) of the subset. For a spher...

Boundary element methods (BEM) reduce a partial differential equation in domain to an integral on the domain’s boundary. They are particularly attractive for solving problems unbounded domains, but handling dense matrices corresponding operators requires efficient algorithms.

Numerical approximations of fractional PDEs in unbounded domains are considered in this paper. Since their solutions decay slowly with power laws at infinity, a domain truncation approach is not effective as no transparent boundary condition is available. We develop efficient Hermite-collocation and Hermite–Galerkin methods for solving a class of fractional PDEs in unbounded domains directly, a...

We prove that an implicit iterative process with errors converges weakly and strongly to a common fixed point of a finite family of asymptotically quasi-nonexpansive mappings on unbounded sets in a uniformly convex Banach space. Our results generalize and improve upon, among others, the corresponding recent results of Sun (2003) in the following two different directions: (i) domain of the mappi...

In this paper we study sharp estimates of pre-Schwarzian derivatives functions belonging to the Nehari-type classes by using techniques from differential equations. sequel, also see that a solution complex equation has special form in terms ratio hypergeometric resulting an integral representation. Finally, attempt those univalent unit disk for which image domain is unbounded John domain.

We prove an analyticity result for the Dirichlet–Neumann operator under space periodic boundary conditions in any dimension unbounded domain with infinite depth. derive analytic bifurcation of Stokes waves—i.e., traveling solutions—of water waves equations deep water.

A new numerical method called high accuracy time and space transform method (TSTM) is introduced to solve the advection–diffusion equation in an unbounded domain. By a spatial transform, the advection– diffusion equation in the unbounded domain Rn is converted to one on the bounded domain [−1,1]n , and the Laplace transform is applied to eliminate time dependency. The consequent boundary value ...

This paper studies the question of resolvent existence, as well as, smoothness elements from definition domain (separability) a class hyperbolic differential operators defined in an unbounded with greatly increasing coefficients after closure space L2(R2). Such problem was previously put forward by I.M. Gelfand for elliptic operators. Here, we note that detailed analysis shows when studying spe...