تم في هذا البحث إثبات وحدانية حل المسألة الخطية الأساسية الأولى لنظرية المرونة الإلكترونية من أجل المنطقة و التي تهدف إلى إيجاد المتجه الذي ينتمي للصف و يحقق جملة المعادلات من أجل بعض الشروط الحدية, و ذلك باستخدام طريقة جديدة تعتمد على محدودية تكامل ديرخليه.
In this research was proofed that the first liner essential
problem of electro Elasticity theory has unique solution .
This problem aim to find the vector which belong to the
class and realize the folowing system of equations :
For som bondary conditions , In improving that the Dairkhli integral
was used .
References used
Martin H . Sadd .,2009 – Elasticity ( Theory , Applications) , Kingston , Rhode Island , 535 p
Kobradze . B ., Gegelia . T ., Bashelshvele . M ., 1976 – Problems of Mathematical Elasticity Theory in the Three Dimensional Space , Mockow , 663 p
Giashi Yang ., 2009 – Special topics in the theory of pizoelectricity . Springer Science + Business Media , USA
In this research paper we found a form of solution for a
system of equations in the couple – stress theory of mathematical
elasticity in the static case and in the neighborhood of a point at
infinity .
And , also , it was proved that the first essential and external
problem of couple-stress theory of elasticity has unique solution.
Most of mathematical physics problems can be translated into solve one
partial differential equation or more with specific initial conditions and
boundary conditions. This is called the boundary value problem for the
differential equations.
This
In this paper we have studied a well known problem called
Jacobian problem, we introduce some new results in
the framework of this problem, we give a
proof to this problem in special case by reducing the resultant of
general polynomial using some MAPLE command. In the same
way, we can deduce the general case.
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.
In this paper, we find distributional solutions of boundary value
problems in Sobolev spaces. This solution will be given as Fourier
series with respect to the Eigen functions of a positive definite
operator and its square roots.
Then, we obtain solutions of such problems of a real order.