We aim in this research to study the existence and uniqueness of strong solution for
initial-boundary values problem for a semi-linear wave equation with the nonlinear
boundary dissipation, by transforming it to a Cauchy problem with second order operator
differential equations in Hilbert space. Therefore, we transform it, using Green's formula
for a triple of Hilbert spaces.
Our aim of this paper is studying the problem on normal oscillations of system of capillary viscous fluids in vessel.
We prove results about the spectrum of the problem for rotating vessel and prove that the systems of root elements ( eigenelements
and associated elements ) form an Abel-Lidsky basis.
Also , we use some results from the theory of J-self adjoint operators in studying the spectrum of the problem for non-rotating vessel.
This work suggests a study of small motions of system of anideal-relaxing fluids which rotate ina limited space. First, we present the problem and reducethe initial boundary value problem that describe it to Cauchy problem for an ordinary differentia
l equation of the second order form in Hilbert space. This allows us to prove the unique solvability theorem.
This Work suggests a study of small motions of system of capillary viscous fluids in rotation vessels ,i.e: to prove the unique solvability theorem of the initial boundary value problem that describe these motions. For that we reduced to Cauchy probl
em that has the form:
Where is a continuous function with values in the Hilbert space E, A is an operator on E,
By using Functional analysis methods (Orthogonal projector, Operator approach,…)
The aim of this paper is to study the spectral problem of small motions of a pendulum with a cavity filled with a system of ideal capillary fluids when the condition of statically stable in linear approximation is valid. It is proved that this proble
m has a real discrete spectrum with a limit point at and the eigenvalues for this problem are successive minima of variation ratio. It is also proved that if the operator of potential energy of a system ( pendulum + a system of ideal capillary fluids )has a negative eigenvalues, then the solutions of the initial boundary value problem are instable
