On solvability of the first initial-boundary value problem for quasilinear pseudoparabolic equations

In the paper, the solvability of the first initial-boundary value problem for a quasilinear pseudoparabolic equationut-Δut-∂∂xibijx,t,uuxj+cix,t,uuxi+ϑx,t,u=fx,twith increasing with respect to ζ functions bijx,t,ζ,cix,t,ζ and ϑx,t,ζ was investigated. The existence and uniqueness of regular solutions are proven.