Increasing Powers in a Degenerate Parabolic Logistic Equation

José Francisco Rodrigues () and Hugo Tavares ()
Additional contact information
José Francisco Rodrigues: Universidade de Lisboa, Department of Mathematics and CMAF
Hugo Tavares: Universidade de Lisboa, Department of Mathematics and CMAF

A chapter in Partial Differential Equations: Theory, Control and Approximation, 2014, pp 379-399 from Springer

Abstract: Abstract The purpose of this paper is to study the asymptotic behavior of the positive solutions of the problem $$\partial_t u-\Delta u=a u-b(x) u^p \quad\text{in } \varOmega\times \mathbb{R} ^+,\quad u(0)=u_0,\quad u(t)|_{\partial \varOmega}=0, $$ as p→+∞, where Ω is a bounded domain, and b(x) is a nonnegative function. The authors deduce that the limiting configuration solves a parabolic obstacle problem, and afterwards fully describe its long time behavior.

Keywords: Parabolic logistic equation; Obstacle problem; Positive solution; Increasing power; subsolution and supersolution; 35B40; 35B09; 35K91 (search for similar items in EconPapers)
Date: 2014
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

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:spr:sprchp:978-3-642-41401-5_15

Ordering information: This item can be ordered from
http://www.springer.com/9783642414015

DOI: 10.1007/978-3-642-41401-5_15

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().