Existence and stability of equilibrium solutions of a nonlinear heat equation

César A. Hernández Melo

Applied Mathematics and Computation, 2014, vol. 232, issue C, 1025-1036

Abstract: The main purpose of this paper is to investigate the existence and stability of periodic and non-periodic equilibrium solutions related to the nonlinear heat equation: (1)ut=uxx+wu+u3+u5.The existence of periodic equilibriums with a fixed period L is deduced from the Theory of Jacobian Elliptical Functions and the Implicit Function Theorem. We show that these periodic equilibriums tend to the non-periodic positive equilibrium solution in the real line. Our stability/instability results are obtained trough the spectral study of the linear operator associated to the linearized stability problem as well as the study of a certain scalar quantity.

Keywords: Nonlinear heat equation; Equilibrium solutions; Elliptic functions; Stability/instability (search for similar items in EconPapers)
Date: 2014
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300314001866
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:232:y:2014:i:c:p:1025-1036

DOI: 10.1016/j.amc.2014.01.140

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().