INITIAL BOUNDARY VALUE PROBLEM FOR SOBOLEV TYPE NONLINEAR EQUATIONS - Mamikonyan, H. A. (Proceedings of the YSU A: Physical and Mathematical Sciences, 2006)
In this paper following initial boundary value problem is considered: cases A(ut)+Bu=f, u(0)=u_0, D^γ|_Γ=0, |γ|≤ m. cases Operators A and B are nonlinear and have the following form: Au=_|α|≤ m(-1)^|α|D^αA_α(x, t, D^γu), Bu=_|α|≤ m(-1)^|α|D^αB_α(x, t, D^γu), |γ|≤ m. Conditions for functions A_α and B_α are obtained that lead to existence and uniqueness of solution of the problem in the spaces L^p(0, T, ^0W^m_p), p≥ 2.