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.

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Attribution 4.0 International

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This work is licensed under a Creative Commons Attribution 4.0 International License.

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