Global existence and finite time blowup for a nonlocal semilinear pseudo-parabolic equation
In this paper, the initial boundary value problem for a nonlocal semilinear pseudo-parabolic equation is investigated, which was introduced to model phenomena in population dynamics and biological sciences where the total mass of a chemical or an organism is conserved. The existence, uniqueness and...
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| Published in | Advances in nonlinear analysis Vol. 10; no. 1; pp. 261 - 288 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
De Gruyter
01.01.2021
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| Subjects | |
| Online Access | Get full text |
| ISSN | 2191-9496 2191-950X |
| DOI | 10.1515/anona-2020-0141 |
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| Abstract | In this paper, the initial boundary value problem for a nonlocal semilinear pseudo-parabolic equation is investigated, which was introduced to model phenomena in population dynamics and biological sciences where the total mass of a chemical or an organism is conserved. The existence, uniqueness and asymptotic behavior of the global solution and the blowup phenomena of solution with subcritical initial energy are established. Then these results are extended parallelly to the critical initial energy. Further the blowup phenomena of solution with supercritical initial energy is proved, but the existence, uniqueness and asymptotic behavior of the global solution with supercritical initial energy are still open. |
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| AbstractList | In this paper, the initial boundary value problem for a nonlocal semilinear pseudo-parabolic equation is investigated, which was introduced to model phenomena in population dynamics and biological sciences where the total mass of a chemical or an organism is conserved. The existence, uniqueness and asymptotic behavior of the global solution and the blowup phenomena of solution with subcritical initial energy are established. Then these results are extended parallelly to the critical initial energy. Further the blowup phenomena of solution with supercritical initial energy is proved, but the existence, uniqueness and asymptotic behavior of the global solution with supercritical initial energy are still open. |
| Author | Xu, Runzhang Wang, Xingchang |
| Author_xml | – sequence: 1 givenname: Xingchang surname: Wang fullname: Wang, Xingchang organization: College of Automation, Harbin Engineering University, 150001, Harbin, People’s Republic of China – sequence: 2 givenname: Runzhang surname: Xu fullname: Xu, Runzhang email: xurunzh@163.com organization: College of Mathematical Sciences, Harbin Engineering University, 150001, Harbin, People’s Republic of China |
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| Title | Global existence and finite time blowup for a nonlocal semilinear pseudo-parabolic equation |
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