and Applied Analysis 3 For every h ∈ L1([0, a],X), the right-hand side of (21) is a continuous function on [0, a]. It is natural to consider it as a generalized solution of (8) even it is not differentiable and dose not strictly satisfy the equation. We therefore define the following. Definition 2. Let −A is the infinitesimal generator of C 0 semigroup T(t) (t ≥ 0). Then a continuous solution u...

The paper presents a new solver for the numerical solution of Boltzmann kinetic equation with Shakhov model collision integral (S-model) arbitrary spatial domains. method utilizes Tucker decomposition, which reduces required computer memory up to 100 times, even on moderate velocity grid. This improvement is achieved by representing distribution function values structured grid as 3D tensor in f...

This paper presents a boundary integral equation method for computing numerical conformal mapping of bounded multiply connected region onto an annulus with spiral slits region and its inverse. The method is an extension of the author’s method for computing the Annulus with circular slits map of bounded multiply connected regions (see [Sangawi, A. W. K., Murid, A. H. M., Nasser, M. M. S.: Annulu...

in this paper, an attempt is made to present an extension of darbo's theorem, and its applicationto study the solvability of a functional integral equation of volterra type.

We have employed our recently developed Green’s function formalism to study the dielectric behavior of a model membrane, formed by two periodic interfaces separating two media of different dielectric constants. The Maxwell’s equations are converted into a surface integral equation; thus it greatly simplifies the solutions and yields accurate results for membranes of arbitrary shape. The integra...