Finite time blow-up for a class of parabolic or pseudo-parabolic equations
dc.contributor.author | Sun, F. | |
dc.contributor.author | Liu, Lishan | |
dc.contributor.author | Wu, Yong Hong | |
dc.date.accessioned | 2018-05-18T07:59:36Z | |
dc.date.available | 2018-05-18T07:59:36Z | |
dc.date.created | 2018-05-18T00:23:29Z | |
dc.date.issued | 2018 | |
dc.identifier.citation | Sun, F. and Liu, L. and Wu, Y.H. 2018. Finite time blow-up for a class of parabolic or pseudo-parabolic equations. Computers and Mathematics with Applications. 75 (10): pp. 3685-3701. | |
dc.identifier.uri | http://hdl.handle.net/20.500.11937/67734 | |
dc.identifier.doi | 10.1016/j.camwa.2018.02.025 | |
dc.description.abstract |
In this paper, we study the initial boundary value problem for a class of parabolic or pseudo-parabolic equations: ut – aΔut − Δu+bu = k(t) |u|p−2u, (x,t) ∈ Ω× (0,T), where a ≥ 0, b >−ł1 with ł1 being the principal eigenvalue for −Δ on H01 (Ω) and k(t) > 0. By using the potential well method, Levine’s concavity method and some differential inequality techniques, we obtain the finite time blow-up results provided that the initial energy satisfies three conditions: (i) J (u0;0) < 0; (ii) J (u0; 0) ≤ d (∞), where d (∞)is a nonnegative constant; (iii) 0 < J (u0;0) ≤ Cρ (0), where ρ (0) involves the L2-norm or H01-norm of the initial data. We also establish the lower and upper bounds for the blow-up time. In particular, we obtain the existence of certain solutions blowing up in finite time with initial data at the Nehari manifold or at arbitrary energy level. | |
dc.publisher | Pergamon Press | |
dc.title | Finite time blow-up for a class of parabolic or pseudo-parabolic equations | |
dc.type | Journal Article | |
dcterms.source.issn | 0898-1221 | |
dcterms.source.title | Computers and Mathematics with Applications | |
curtin.department | School of Electrical Engineering, Computing and Mathematical Science (EECMS) | |
curtin.accessStatus | Fulltext not available |
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