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Mathematics

Method of Galyorkin for nonlinear Sobolev type equations

R. Lotfikar<sup>ab

a</sup> Yerevan State University
^b Islamic Azad University, Tehran

Abstract: In this paper the following initial boundary value problem is considered:
$$\left\{
\begin{array}{l} L\left(\frac{\partial u(t,x)}{\partial t}\right)+Mu(t,x)=f(t,x),\\ u(0,x)=u_0(x),\\ D^{\gamma}u\Big|_{\tilde A}=0, |\gamma|<m,\end{array}
\right.$$
$L$ and $M$ are nonlinear differential operators.
It is proved that if $L$ and $M$ satisfy to some conditions, then the sequence constructed by solutions of Galyorkin’s equations for this problem is convergence to the week solution of the problem

UDC: 517.9

Received: 29.01.2008