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
Keywords
Related Articles
- EP ID EP342740
- DOI -
- Views 86
- Downloads 0
The plane mixed elastical problem for the semi-infinite strip
The loaded plane elastic semistrip, the one boundary of which is fixed and the second one is in the smooth contact condition, is considered. The solution of the problem in −sin, −cos Fourier transformant’s domain is cons...
THE ANALOGUE OF THE FLOQUET-LYAPUNOV THEOREM FOR THE LINEAR DIFFERENTIAL SYSTEMS OF THE SPECIAL KIND
The analogue of the well known in the theory of the linear differential systems Floquet's--Lyapunov's theorem are constructed by the certain condidtions for the linear differential system, whose coefficients are represen...
Boundary value problems with impulsive “interface conditions” action and lumped delay
Linear nonhomogeneous differential equations with variable concentrated delay and impulsive influence of “interface condition” type with known boundary condition is considered.Conditions of existence and uniqueness of co...
Variational method of homogeneous solutions for axisymmetric elasticity problems
A variational method of homogeneous solutions for solving of axisymmetric elasticity problems for semiinfinite and finite cylinders with free lateral surface has been developed. As an example of application of the method...
Averaging of differential equations of movement for the ship on the direct course
The possibility of applying the full averaging scheme to the ship complex control problem is considered in the article. The model of this problem was first described by V. I. Nebesnov and V. A. Plotnikov and F. Y. Kuzyu...