METHOD OF GALYORKIN FOR NONLINEAR SOBOLEV TYPE EQUATIONS
DOI:
https://doi.org/10.46991/PYSU:A/2008.42.3.010Keywords:
Galyorkin’s equations, Sobolev type equations, initial boundary value problemAbstract
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
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Mathematics
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