Hyperbolic equation with singular coefficient
Journal Title: Дослідження в математиці і механіці - Year 2017, Vol 22, Issue 1
Abstract
Dedicated to research existence conditions of quasi-linear differential equations with measurable coefficients, ie the study limitations imposed by the non linearity in which the system will have to research a solution and uniqueness of the solution of a certain class of functions. We consider weak solvability of quasi-linear differential partial differential equations of hyperbolic type with smooth and measurable singular coefficients, research methods based on the theory of semigroups using the method of differential forms. A new class of operators 𝐴𝑝 𝜆 : 𝑊𝑝 1 → 𝑊𝑝 −1 associated with a given differential equation and investigate the properties of these operators.
Authors and Affiliations
M. I. Yaremenko
Partial averaging of the systems on time scales
The scheme of partial averaging of systems with small parameter on time scales was established. A proximity of solutions of given and partially averaged system of equations was proved under sufficiently general condition...
On an adaptive method of regulator parameters adjustment at discrete time points
We offer an adaptive method of regulator parameters correction at discrete points of time. The method is based on the following idea: we choose the parameters of the parametric regulator at discrete moments of time minim...
On some nonlocal boundary value problems for nonlinear ordinary differential equations with delay
The results of this paper were reported at International Workshop “Nonlinear Analysis and Nonautonomous Ordinary Differential Equations” (Odessa, Ukraine, June 23-27, 2017). In the paper, nonlocal boundary value problems...
INVESTIGATION OF THE NON-STATIONARY THERMOELASTIC STATE OF SHELLS COMPLIANT TO SHEARS AND COMPRESSION
A linear boundary-value problem for thin shells compliant to shears and compression (a six-modal variant) is formulated. The key equations for determining the non-stationary thermoelastic state of the considered shells a...
COMPARISON THEOREM FOR NEUTRAL STOCHASTIC INTEGRO-DIFFERENTIAL EQUATIONS IN HILBERT SPACE
In the present paper, we will discuss a comparison result for solutions to the Cauchy problems for two stochastic differential equations with delay. On this subject number of authors have obtained their comparison result...