Shell structures are widely used in various fields of technology and construction. Often, they play the role a bearing surface with assemblies, overlays, aggregates installed on them. At same time, solving problems, such attached elements considered as concentrated at points rigidly connected. Vibrations an orthotropic viscoelastic shallow shell masses geometrically nonlinear setting considered...

We investigate the oscillatory chemical dynamics in a closed isothermal reaction system described by the reversible Lotka-Volterra model. This is a three-dimensional, dissipative, singular perturbation to the conservative Lotka-Volterra model, with the free energy serving as a global Lyapunov function. We will show that there is a natural distinction between oscillatory and non-oscillatory regi...

A two-grid temporal second-order scheme for the two-dimensional nonlinear Volterra integro-differential equation with a weakly singular kernel is of concern in this paper. The targeted to reduce computation time and improve accuracy developed by Xu et al. (Appl Numer Math 152:169–184, 2020). constructed armed three steps: First, small system solved on coarse grid using fix-point iteration. Seco...

In this paper it is shown that the use of‎ ‎uniform meshes leads to optimal convergence rates provided that‎ ‎the analytical solutions of a particular class of‎ ‎Fredholm-Volterra integral equations (FVIEs) are smooth‎.

0 gi(t, s)[Pi(s, u1(s), u2(s), · · · , un(s)) + Qi(s, u1(s), u2(s), · · · , un(s))]ds, t ∈ [0, T ], 1 ≤ i ≤ n where T > 0 is fixed and the nonlinearities Pi(t, u1, u2, · · · , un) can be singular at t = 0 and uj = 0 where j ∈ {1, 2, · · · , n}. Criteria are offered for the existence of fixed-sign solutions (u∗1, u ∗ 2, · · · , u ∗ n) to the system of Volterra integral equations, i.e., θiu ∗ i (...

We suggest an elementary harmonic analysis approach to canceling and weakly differential operators, which allows us extend these notions the anisotropic setting replace operators with Fourier multiplies mild smoothness regularity. In this more general of multipliers, we prove inequality $$\|f\|_{L_\infty} \lesssim \|Af\|_{L_1}$$ if $$A$$ is a operator order $$d$$ $$\|f\|_{L_2} $$d/2$$ , provide...

We define and solve Volterra equations driven by an irregular signal, by means of a variant of the rough path theory called algebraic integration. In the Young case, that is for a driving signal with Hölder exponent γ > 1/2, we obtain a global solution, and are able to handle the case of a singular Volterra coefficient. In case of a driving signal with Hölder exponent 1/3 < γ ≤ 1/2, we get a lo...

This paper concerns the integral equation

in this article, we develop the sinc-galerkin method based on double exponential transformation for solving a class of weakly singular nonlinear two-point boundary value problems with nonhomogeneous boundary conditions. also several examples are solved to show the accuracy efficiency of the presented method. we compare the obtained numerical results with results of the other existing methods in...