A two-parameter shooting problem for a second-order differential equation
type: Item
instance of: scholarly article
title: A two-parameter shooting problem for a second-order differential equation
zbMATH Open document ID: 0810.34024
author: Thierry Cazenave
author: M. Escobedo
published in: Journal of Differential Equations
publication date: 1994-10-24T00:00:00Z
review text: The author considers the nonlinear equation \(u''+ p| u|^{p-1} u'+ {t\over 2} u'+ {1\over 2(p-1)} u=0\), \(t\in \mathbb{R}\), under the conditions \(\lim_{t\to+\infty} u(t)=0\), \(\lim_{t\to -\infty} (- t)^{-1/(p-1)} u(t)= p^{-1/(p-1)}\), \(u\geq 0\), and show that when \(1< p<2\) its global solutions constitute a one-parameter ordered family \((u^ \lambda)\) with \(\lambda\geq 0\). They show also that the global solution which behaves like \(\exp\{-t^ 2/4\}\) is unique and \(u^ 0\). To arrive at the result they are based on 23 propositions, lemmas and corollaries. Notice that this particular equation and boundary conditions play an important role in the study of the long-time behavior of a nonlinear diffusion phenomenon.
Mathematics Subject Classification ID: 34C11
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 665708
zbMATH Keywords: nonlinear equation
zbMATH Keywords: global solutions
zbMATH Keywords: nonlinear diffusion phenomenon
reviewed by: Mithat Idemen
MaRDI profile type: Publication
full work available at URL: jdeq.1994.1131
OpenAlex ID: W1992360154
DOI: 10.1006/JDEQ.1994.1131
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description: scientific article; zbMATH DE number 665708