Kaikina, Elena I.2021-08-172021-08-172007-08-07Kaikina, E. I. (2007). Initial-boundary value problems for nonlinear pseudoparabolic equations in a critical case. <i>Electronic Journal of Differential Equations, 2007</i>(109), pp. 1-11.1072-6691https://hdl.handle.net/10877/14325We study nonlinear pseudoparabolic equations, on the half-line in a critical case, ∂t(u - uₓₓ) - αuₓₓ = λ|u|u, x ∈ ℝ⁺, t > 0, u(0, x) = u0(x), x ∈ ℝ⁺, u(t, 0) = 0, where α > 0, λ ∈ ℝ. The aim of this paper is to prove the existence of global solutions to the initial-boundary value problem and to find the main term of the asymptotic representation of solutions.Text25 pages1 file (.pdf)enAttribution 4.0 InternationalDissipative nonlinear evolution equationSobolev equationLarge time asymptotic behaviorArticleThis work is licensed under a Creative Commons Attribution 4.0 International License.