Name
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. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1016/j.camwa.2018.02.025 | Computers & Mathematics with Applications |
Keywords | Field | DocType |
Parabolic equation,Pseudo-parabolic equation,Concavity method,Blow-up,Life span | Parabolic partial differential equation,Boundary value problem,Differential inequalities,Nehari manifold,Blowing up,Mathematical analysis,Mathematics,Eigenvalues and eigenvectors,Parabola,Finite time | Journal |
Volume | Issue | ISSN |
75 | 10 | 0898-1221 |
Citations | PageRank | References |
2 | 0.45 | 3 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Fenglong Sun | 1 | 5 | 1.00 |
| Lishan Liu | 2 | 188 | 35.41 |
| Yonghong Wu | 3 | 212 | 34.70 |