Subcritical nonlinear nonlocal equations on a half-line
type: Item
instance of: scholarly article
title: Subcritical nonlinear nonlocal equations on a half-line
zbMATH Open document ID: 1080.35166
author: Elena I. Kaikina
published in: Journal of Mathematical Analysis and Applications
publication date: 2005-04-21T00:00:00Z
review text: The author studies nonlinear nonlocal equations on a half-line in the subcritical case \[ \begin{aligned} \partial_tu +\beta| u| ^pu+Ku=0, &\quad x>0,\;t >0,\\ u(0,x) = u_0(x), &\quad x > 0, \tag{1}\\ \partial_x^{j-1}u(0,t) = 0, &\quad j= 1,\dots,M, \end{aligned} \] where \(\beta\in {C},\rho\in(0,\alpha).\) The linear operator \(K\) is a pseudodifferential operator defined by the inverse Laplace transform with dissipative symbol \(K(p) = E_{\alpha}p^{\alpha}\), the number \(M = [\frac{\alpha}{2}]\). The author proves the global existence of solutions to the initial-boundary value problem (1) and finds the main term of the large time asymptotic representation of solutions in the subcritical case, when the time decay rate of the nonlinearity is less than that of the linear part of the equation.
Mathematics Subject Classification ID: 35R10
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 35S05
zbMATH DE Number: 2159793
zbMATH Keywords: nonlinear nonlocal equation
zbMATH Keywords: global existence
zbMATH Keywords: large time asymptotic
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.11.063
OpenAlex ID: W1982320641
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DOI: 10.1016/J.JMAA.2004.11.063
description: scientific article; zbMATH DE number 2159793