Header only for the first page

Question

The header is printed on the first page only as I need, but the header box (empty) still present on other pages. How to get rid of it?

\documentclass[a4paper,10pt,twoside,titlepage]{article}
\usepackage[T2A]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{amsmath,amssymb,amscd,amsfonts,amsthm,cite,mathrsfs,indentfirst,hyperref}
\usepackage{graphicx,graphics,pstricks,pst-plot,caption,subcaption,booktabs,setspace,textcomp,pspicture}
\usepackage[russian,english]{babel}
%\usepackage[headheight=30pt]{geometry}

\numberwithin{equation}{section}


%--------------- Page Geometry---------------
\usepackage{anysize}
\marginsize{4.0cm}{4.0cm}{4.0cm}{4.0cm}
%\topmargin=-1.0cm
\renewcommand{\baselinestretch}{1.0}
%--------------------------------------------



\usepackage{fancyheadings}


%\lfoot{}\cfoot{}\rfoot{\thepage}

\pagenumbering{arabic}

\begin{document}

\setlength{\headheight}{30pt}

\thispagestyle{fancy}
\lhead{}\chead{Some Text\\ \noindent\makebox[\linewidth]{\rule{\textwidth}{0.4pt}}\\ Mechanics~~~~~~~~~~~~{\hfill Volume 69, Issue 1, 2015 \hfill}\hfill Mechanics}\rhead{}
\renewcommand{\headrulewidth}{0pt} 


\noindent\textbf{UDC 517.977.1+517.977.5}

\begin{center} \textbf{GREEN`S FUNCTION APPROACH IN APPROXIMATE CONTROLLABILITY PROBLEMS} \end{center}

\begin{center} \textbf{Khurshudyan As. Zh.} \end{center}

A mathematical method based on Green`s function approach widely used, in particular, for solving problems in mathematical physics and deformable body mechanics which allows to construct controls providing approximate controllability is suggested in the present paper. Representing the solution of governing system via Green’s formula and forcing the controlled state function to satisfy required terminal conditions, we obtain implicit representation for admissible controls. Choosing appropriate controls, we can provide required accuracy of approximation for terminal condition. Particularly, infinite string controlled by a concentrated force and semi-infinite rod heated by a point heat source are considered. Examples illustrating the procedure are described. Results of numerics are brought.

A mathematical method based on Green`s function approach widely used, in particular, for solving problems in mathematical physics and deformable body mechanics which allows to construct controls providing approximate controllability is suggested in the present paper. Representing the solution of governing system via Green’s formula and forcing the controlled state function to satisfy required terminal conditions, we obtain implicit representation for admissible controls. Choosing appropriate controls, we can provide required accuracy of approximation for terminal condition. Particularly, infinite string controlled by a concentrated force and semi-infinite rod heated by a point heat source are considered. Examples illustrating the procedure are described. Results of numerics are brought.

A mathematical method based on Green`s function approach widely used, in particular, for solving problems in mathematical physics and deformable body mechanics which allows to construct controls providing approximate controllability is suggested in the present paper. Representing the solution of governing system via Green’s formula and forcing the controlled state function to satisfy required terminal conditions, we obtain implicit representation for admissible controls. Choosing appropriate controls, we can provide required accuracy of approximation for terminal condition. Particularly, infinite string controlled by a concentrated force and semi-infinite rod heated by a point heat source are considered. Examples illustrating the procedure are described. Results of numerics are brought.



\end{document}

Answer 1

If I understand your setup correctly, there's actually no need to define a header block just for the first page. Instead, I suggest you do something like the following.

\documentclass[a4paper,10pt,twoside,titlepage]{article}
\usepackage[T2A]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage[russian,english]{babel}

\usepackage{anysize}
\marginsize{4.0cm}{4.0cm}{4.0cm}{4.0cm}

\pagenumbering{arabic}

\begin{document}

\begin{center}
HAYASTANI GITUT'YUNNERI AZGAYIN AKADEMIAYI TEGHEKAGIR

PROCEEDINGS OF NATIONAL ACADEMY OF SCIENCES OF ARMENIA
\smallskip
\hrule 
\smallskip

Mexanika \hfill Volume 69, Issue 1, 2015 \hfill Mechanics
\end{center}

\noindent\textbf{UDC 517.977.1+517.977.5}

\begin{center}
\bfseries GREEN'S FUNCTION APPROACH IN 

APPROXIMATE CONTROLLABILITY PROBLEMS

\bigskip
\textbf{Khurshudyan As. Zh.} 
\end{center}

A mathematical method based on Green's function approach widely used, in particular, for solving problems in mathematical physics and deformable body mechanics which allows to construct controls providing approximate controllability is suggested in the present paper. Representing the solution of governing system via Green’s formula and forcing the controlled state function to satisfy required terminal conditions, we obtain implicit representation for admissible controls. Choosing appropriate controls, we can provide required accuracy of approximation for terminal condition. Particularly, infinite string controlled by a concentrated force and semi-infinite rod heated by a point heat source are considered. Examples illustrating the procedure are described. Results of numerics are brought.

\end{document}

Answer 2

Since you say that the bit of text is part of the title, not actually a heading ... don't use the mechanism to generate a heading.

Do it like you would do it with any other title, add a bit of space by hand.

\documentclass[a4paper,10pt,twoside]{article}
\usepackage{blindtext}

%--------------- Page Geometry---------------
\usepackage{geometry}
\geometry{margin=4cm}

\begin{document}

\begin{center}
    \vspace*{-2cm}
    Some text\\
    {\rule[1ex]{\textwidth}{0.4pt}}\\
    Mechanics~~~~~~~~~~~~{\hfill Volume 69, Issue 1, 2015
    \hfill}\hfill Mechanics
    \par
    \vspace{1.5cm}

    \textbf{UDC 517.977.1+517.977.5}\bigbreak

    \textbf{GREEN'S FUNCTION APPROACH IN APPROXIMATE
    CONTROLLABILITY PROBLEMS}\bigbreak

    \textbf{Khurshudyan As. Zh.}
\end{center}

\blindtext

\blindtext

\blindtext

\end{document}