Blow-up of solutions for a system of nonlocal singular viscoelastic equations

The main propose of this paper is to study the blow-up of solutions of an initial boundary value problem with a nonlocal boundary condition for a system of nonlinear singular viscoelastic equations. where the blow-up of solutions in finite time with nonpositive initial energy combined with a positive initial energy are shown.     

Stability of neutral stochastic functional differential equations with Markovian switching driven by G-Brownian motion

Little seems to be known about stability results on the neutral stochastic function differential equations with Markovian switching driven by G-Brownian (G-NSFDEwMSs). This paper aims at investigating the pth moment exponential stability for G-NSFDEwMSs to fill this gap. Some sufficient conditions on the pth moment exponential stability of the trivial solution are derived by employing the Razumikhin-type method, stochastic analysis, and algebraic inequality technique. Moreover, an example is provided to illustrate the effectiveness of the obtained results.     

Time‐harmonic and asymptotically linear Maxwell equations in anisotropic media

This paper is focused on following time‐harmonic Maxwell equation: where is a bounded Lipschitz domain, is the exterior normal, and ω is the frequency. The boundary condition holds when Ω is surrounded by a perfect conductor. Assuming that f is asymptotically linear as , we study the above equation by improving the generalized Nehari manifold method. For an anisotropic material with magnetic permeability tensor and permittivity tensor , ground state solutions are established in this paper. Applying the principle of symmetric criticality, we find 2 types of solutions with cylindrical symmetries in particular for the uniaxial material.     

On Grassmannizable Group 3-Webs

The authors prove that the Lie group G generating a Grassmannizable group 3-web GGW is the group of parameters of the group of similarity transformations of an (r−1)-dimensional affine space . The transitive action of the group G on itself is an r-parameter subgroup B(r) of the group A(r ²+r) of affine transformations z ^I =a _J ^I x ^J +b ^I ,I,J=1,…,r, which is the direct product of the one-dimensional group of homotheties z ¹=kx ¹ and r−1 one-dimensional groups of affine transformations where all r groups have the same homothety coefficient k. Conversely, the Lie group B(r) described above generates a Grassmannizable group 3-web GGW. The Lie group G is solvable but not nilpotent.      

Blow-up analysis for a system of heat equations with nonlinear flux which obey different laws

We consider a system of heat equations u_t=Δu and v_t=Δv in Ω×(0,T) completely coupled by nonlinear boundary conditions

We prove that the solutions always blow up in finite time for non-zero and non-negative initial values. Also, the blow-up only occurs on ∂Ω with

for p,q>0, 0≤α<1 and 0≤β<p.     

Approximation theorems for localized szsz–Mirakjan operators

In the present paper, we investigate the convergence and the approximation order of the localized Szsz–Mirakjan operators, and obtain some new results to improve the results due to Omey [Note on operators of Szsz–Mirakjan type, J. Approx. Theory 47 (1986) 246–254].     

Controllability results for a class of one-dimensional degenerate parabolic problems in nondivergence form

We give null controllability results for some degenerate parabolic equations in non divergence form on a bounded interval. In particular, the coefficient of the second order term degenerates at the extreme points of the domain. For this reason, we obtain an observability inequality for the adjoint problem. Then we prove Carleman estimates for such a problem. Finally, in a standard way, we deduce null controllability also for semilinear equations.      

Group decisions I. In arbitrary spaces of fuzzy binary relations

This article solves the problem of finding a set of group decisions that satisfy the classical Pareto unanimity principle for the case of initial data represented as fuzzy relations of individual preference. The solution proceeds from results obtained in studying the structure of convex (in the sense defined here) sets and their convex hulls. In the first part that study is carried out for spaces of arbitrary fuzzy binary relations.     

An application of the generalized alternating polynomials to the numerical solution of Fredholm integral equations

Generalized alternating polynomials have been introduced by the author earlier. In the present paper their indirect analogue is constructed for numerical solution of the Fredholm linear integral equations. Although the proposed method is a particular case of the general projection scheme, its valuable feature is the presence of a sequence of parameters, which, for sufficiently smooth kernels and inhomogeneous terms, serves as an indicator of the quality of approximation.     

Some applications of Briot—Bouquet differential subordination

Some applications of Briot—Bouquet differential subordination are obtained which improve or extend a number of classical results in the univalent function theory.