Fringing field can prevent infinite time quenching. (August 2016)
- Record Type:
- Journal Article
- Title:
- Fringing field can prevent infinite time quenching. (August 2016)
- Main Title:
- Fringing field can prevent infinite time quenching
- Authors:
- Pan, Hongjing
Xing, Ruixiang - Abstract:
- Abstract: Consider the following problem arising in Micro-Electro-Mechanical Systems (MEMS) { u t − Δ u = λ ( 1 + δ ∣ ∇ u ∣ 2 ) ( 1 − u ) p, ( x, t ) ∈ Ω × ( 0, T ), u = 0, ( x, t ) ∈ ∂ Ω × ( 0, T ), u ( x, 0 ) = u 0 ( x ), 0 ⩽ u 0 ( x ) < 1, x ∈ Ω, where δ > 0, p > 1 and Ω is a bounded smooth domain in R N ( N ⩾ 1 ) . We prove that infinite time quenching is impossible for any λ > 0 in this problem. It provides a remarkable contrast to the case of δ = 0, in which infinite time quenching must happen for some λ when Ω is a ball in R N ( N ⩾ 8 ) . This means that the presence of the fringing field δ | ∇ u | 2 dramatically changes the quenching behavior of the solution. We also obtain some new results about global convergence and quenching in finite time.
- Is Part Of:
- Nonlinear analysis. Volume 30(2016)
- Journal:
- Nonlinear analysis
- Issue:
- Volume 30(2016)
- Issue Display:
- Volume 30, Issue 2016 (2016)
- Year:
- 2016
- Volume:
- 30
- Issue:
- 2016
- Issue Sort Value:
- 2016-0030-2016-0000
- Page Start:
- 126
- Page End:
- 142
- Publication Date:
- 2016-08
- Subjects:
- Quenching -- Singular nonlinearity -- Fringing field -- Gradient quadratic growth -- MEMS -- Global convergence -- Convex nonlinearity
Nonlinear functional analysis -- Periodicals
Analyse fonctionnelle non linéaire -- Périodiques
Nonlinear functional analysis
Periodicals
515.7248 - Journal URLs:
- http://www.sciencedirect.com/science/journal/14681218 ↗
http://www.elsevier.com/journals ↗ - DOI:
- 10.1016/j.nonrwa.2015.12.004 ↗
- Languages:
- English
- ISSNs:
- 1468-1218
- Deposit Type:
- Legaldeposit
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library DSC - 6117.315200
British Library DSC - BLDSS-3PM
British Library HMNTS - ELD Digital store - Ingest File:
- 2230.xml