Pullback Permanence for Non-Autonomous Partial Differential Equations
| dc.contributor.author | Langa, Jose A. | |
| dc.contributor.author | Suarez, Antonio | |
| dc.date.accessioned | 2020-08-17T18:25:31Z | |
| dc.date.available | 2020-08-17T18:25:31Z | |
| dc.date.issued | 2002-08-08 | |
| dc.description.abstract | A system of differential equations is permanent if there exists a fixed bounded set of positive states strictly bounded away from zero to which, from a time on, any positive initial data enter and remain. However, this fact does not happen for a differential equation with general non-autonomous terms. In this work we introduce the concept of pullback permanence, defined as the existence of a time dependent set of positive states to which all solutions enter and remain for suitable initial time. We show this behaviour in the non-autonomous logistic equation ut - Δu = λu - b(t)u3, with b(t) > 0 for all t ∈ ℝ, lim t→∞ b(t) = 0. Moreover, a bifurcation scenario for the asymptotic behaviour of the equation is described in a neighbourhood of the first eigenvalue of the Laplacian. We claim that pullback permanence can be a suitable tool for the study of the asymptotic dynamics for general non-autonomous partial differential equations. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 20 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Langa, J. A., & Suarez, A. (2002). Pullback permanence for non-autonomous partial differential equations. <i>Electronic Journal of Differential Equations, 2002</i>(72), pp. 1-20. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/12405 | |
| dc.language.iso | en | |
| dc.publisher | Southwest Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2002, San Marcos, Texas: Southwest Texas State University and University of North Texas. | |
| dc.subject | Non-autonomous differential equations | |
| dc.subject | Pullback attractors | |
| dc.subject | Comparison techniques | |
| dc.subject | Performance | |
| dc.title | Pullback Permanence for Non-Autonomous Partial Differential Equations | |
| dc.type | Article |