METHOD OF GALYORKIN FOR NONLINEAR SOBOLEV TYPE EQUATIONS - Lotfikar, R. (Proceedings of the YSU A: Physical and Mathematical Sciences, 2023)
In this paper the following initial boundary value problem is considered: cases L (u(t, x)t)+Mu (t, x) = f (t, x), u(0, x)=u_0(x), D^γu|_Γ=0, |γ|<m, 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.