Qualitative properties of the fourth-order hyperbolic equations

We investigate the qualitative properties of the weak solutions to the boundary value problems for the hyperbolic fourth-order linear equations with constant coefficients in the plane bounded domain convex with respect to characteristics. The main question is to prove the analogue of maximum principle, solvability and uniqueness results for the weak solutions of initial and boundary value problems in the case of weak regularities of initial data from $L^2.$Comment: arXiv admin note: substantial text overlap with arXiv:2308.0364

Inhomogeneity of the first and second statistical moments of stresses inside the heterogeneities of random structure matrix composites

AbstractIn this paper linearly thermoelastic composite media are treated, which consist of a homogeneous matrix containing a statistically homogeneous random set of heterogeneities. Effective properties (such as compliance, thermal expansion, stored energy) as well as the first statistical moments of stresses in the phases are estimated for the general case of nonhomogeneity of the thermoelastic inclusion properties. The micromechanical approach is based on the generalization of the “multiparticle effective field” method (MEFM, see for references Buryachenko, Appl. Mech. Rev. (2001), 54, 1–47), previously proposed for the estimation of stress field averages in the phases. The method exploits as a background the new general integral equation proposed by the author before and makes it possible to abandon the use of the central concept of classical micromechanics such as effective field hypothesis as well as their satellite hypothesis of “ellipsoidal symmetry”. The implicit recursion representations of the effective thermoelastic properties and stress concentration factor are expressed through some building blocks described by numerical solutions for both the one and two inclusions inside the infinite medium subjected to the inhomogeneous effective fields evaluated from subsequent self-consistent estimations. One also estimates the inhomogeneous statistical moments of local stress fields which are extremely useful for understanding the evolution of nonlinear phenomena such as plasticity, creep, and damage. Just at some additional assumptions (such as an effective field hypothesis) the involved tensors can be expressed through the Green function, Eshelby tensor and external Eshelby tensor. These estimated inhomogeneities of effective fields lead to the detection of fundamentally new effects for the local stresses inside the heterogeneities

Maximum principle for the weak solutions of the Cauchy problem for the fourth-order hyperbolic equations

We investigate the maximum principle for the weak solutions to the Cauchy problem for the hyperbolic fourth-order linear equations with constant complex coefficients in the plane bounded domai

Local sub-estimates of solutions to double phase parabolic equations via nonlinear parabolic potentials

For parabolic equations with nonstandard growth conditions, we prove local boundedness of weak solutions in terms of nonlinear parabolic potentials of the right-hand side of the equation

Reputation as a factor of inter-party competition

An understanding of the reputation of the political party as a socio-political phenomenon is considered. It is shown that managing the reputation of a political party is an important prerequisite for political success. The factors of reputation of a political party, which make up a competitive field in inter-party relations during the pre-election period, are analyzed. The approaches to determining the reputation structure of a political party are described.Key words: reputation, political party, reputation structure, reputation factors

Neumann problem in a disk for fourth-order improperly elliptic equations

We have established and investigated the sufficient conditions of solvability of the Neumann problem for all classes of fourth-order improperly elliptic equatios in a unit disk K in the space C⁴(K) ∩ C³,ª(K)