 Stability AnalysisC. V. Pao
Chapter Chapter 5 in Nonlinear Parabolic and Elliptic Equations, 1992, pp 183-227 from Springer Abstract: Abstract The existence of upper and lower solutions for the elliptic boundary-value problem ensures the existence of at least one steady-state solution. By constructing a suitable pair of upper and lower solutions for the parabolic boundary-value problem it is sometimes possible to determine whether the steady-state solution is stable or unstable. This construction leads to various sufficient conditions for the stability or instability of a given steady-state solution. When the initial function in the parabolic problem is an upper solution or a lower solution of the corresponding elliptic problem the time-dependent solution is monotone in t and converges to a steady-state solution. This monotone convergence property gives a close relationship between the stability and the uniqueness property of a steady-state solution and is a basic tool for determining the stability property of the maximal and the minimal solutions when there are multiple steady-state solutions. These results are applied to a number of specific models that involve either linear or nonlinear boundary conditions. Keywords: Asymptotic Stability; Stability Region; Trivial Solution; Lower Solution; Reaction Function (search for similar items in EconPapers) There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4615-3034-3_5 Ordering information: This item can be ordered from DOI: 10.1007/978-1-4615-3034-3_5 Access Statistics for this chapter More chapters in Springer Books from Springer |
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