It has been proven that the solution to the Dirichlet problem in a circle, where the boundary is specified as F2(x1; x2) = 0, F2(x1; x2) being a polynomial of degree 2, and the boundary function is specified as Qm(x1; x2), Qm(x1; x2) being a polynomial of degree m, admits representation u(x1; x2) = F2(x1; x2) Pm
An modeling attempt of behavior process of brain electric impulses for some patient by the solutions of 3D system of quadratic differential equations is undertaken. (This system of differential equations was got from a multivariate times series with the help of polynomial averages and least square method.) Transition conditions from a chaotic attractor to a limit cycle (and vice versa) of the system of differential equations are found. Exactly these conditions characterize beginning of process of disease by Parkinson’s illness at the patient.
We discuss the H¨older continuity property for the inverse mapping that identifies the diffusivity matrix A(x) in the main part of anisotropic p-Laplace equation as a function of resolvent operator. In particular, we prove that, within a chosen class of non-smooth admissible matrices the resolvent determines the anisotropic diffusivity in a unique manner and the correspondent inverse mapping is H¨older continuous in suitable topologies.
New necessary and sufficient solvability conditions of a linear output feedback design problem for linear control system are offered. With the help of got conditions a solution of robust regulator design problem for the linear control system is also
shown. Examples are given.
We discuss solvability and some extra regularity properties for the weak solutions to one class of the initial-boundary value problem arising in the study of the dynamics of an arterial system.
The approximated method of solving two-dimensional non-linear problem of the creep theory for viscoelastic bodies with moving boundaries is suggested. The problem of a stress-deformed state of viscoelastic hollow cylinder, which is being built up by virtue of inner pressure, is considered. It is assumed that the process of continuous build-up takes place outwards from the outer side. The case of onliner creep law is viewed with calculation results presented as graphs, reflecting the dynamics of stress and deformation that occurs herewith.
The present paper deals with behaviour of approximate solution sequence of boundary problems for the nonlinear elliptic equations of von Karman type constructed with the employment of the iterative generalized Kantorovich method; the relations for the generalized solution of equations in question is used as the governing ones. We revealed correctness of the relations as well as strongly continuity of the method operator in specific ’weighted’ space that makes it possible to state sufficient conditions for strong convergence.
The research deals with the mathematical model of multivariate testing of the landing page of the website. The confidence intervals for the conversion rate difference of the landing page variations are investigated.
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