Bounds for blow-up time in a semilinear pseudo-parabolic equation with nonlocal source
Abstract This paper considers the following semilinear pseudo-parabolic equation with a nonlocal source: u t − △ u t − △ u = u p ( x , t ) ∫ Ω k ( x , y ) u p + 1 ( y , t ) d y , $$ u_{t}-\triangle u_{t}-\triangle u=u^{p}(x,t) \int_{\Omega}k(x,y)u^{p+1}(y,t)\,dy, $$ and it explores the characters of...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2016-09-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-016-1171-4 |
| Summary: | Abstract This paper considers the following semilinear pseudo-parabolic equation with a nonlocal source: u t − △ u t − △ u = u p ( x , t ) ∫ Ω k ( x , y ) u p + 1 ( y , t ) d y , $$ u_{t}-\triangle u_{t}-\triangle u=u^{p}(x,t) \int_{\Omega}k(x,y)u^{p+1}(y,t)\,dy, $$ and it explores the characters of blow-up time for solutions, obtaining a lower bound as well as an upper bound for the blow-up time under different conditions, respectively. Also, we investigate a nonblow-up criterion and compute an exact exponential decay. |
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| ISSN: | 1029-242X |