METHOD OF GALYORKIN FOR NONLINEAR SOBOLEV TYPE EQUATIONS

Authors

  • R. Lotfikar Chair of the Optimal Control Theory and Approximate Methods, YSU, Armenia, Ilam Azad University, Iran

DOI:

https://doi.org/10.46991/PYSU:A/2008.42.3.010

Keywords:

Galyorkin’s equations, Sobolev type equations, initial boundary value problem

Abstract

In this paper the following initial boundary value problem is considered: $$ \begin{cases}  L \left(\dfrac{\partial u(t, x)}{\partial t}\right)+Mu (t, x) = f (t, x), \\ u(0, x)=u_0(x), \\ D^{\gamma}u|_{\Gamma}=0, |\gamma|<m,  \end{cases}$$  where $L$ 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.

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Published

2023-10-06

How to Cite

Lotfikar, R. (2023). METHOD OF GALYORKIN FOR NONLINEAR SOBOLEV TYPE EQUATIONS. Proceedings of the YSU A: Physical and Mathematical Sciences, 42(3 (217), 10–15. https://doi.org/10.46991/PYSU:A/2008.42.3.010

Issue

Section

Mathematics