Initial-boundary value problems for nonlinear pseudoparabolic equations in a critical case
Date
2007-08-07
Authors
Kaikina, Elena I.
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
Abstract
We 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.
Description
Keywords
Dissipative nonlinear evolution equation, Sobolev equation, Large time asymptotic behavior
Citation
Kaikina, 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.
Rights
Attribution 4.0 International
Rights Holder
This work is licensed under a Creative Commons Attribution 4.0 International License.