Nonlinear pseudoparabolic type equations on a half-line with large initial data

We study nonlinear pseudoparabolic type equations on a half-line {∂t(u−uxx)−αuxx=λ|u|σu,x∈R+,t>0,u(0,x)=u0(x),x∈R+,u(t,0)=0, where α>0,σ>0,λ∈R. The aim of this paper is to prove the global existence of solutions to the initial–boundary value problem and to find the main term of the asymptotic representation of the solutions.