Blowup and asymptotic stability of weak solutions to wave equations with nonlinear degenerate damping and source terms
| dc.contributor.author | Hu, Qingying | |
| dc.contributor.author | Zhang, Hongwei | |
| dc.date.accessioned | 2021-08-11T18:05:53Z | |
| dc.date.available | 2021-08-11T18:05:53Z | |
| dc.date.issued | 2007-05-22 | |
| dc.description.abstract | This article concerns the blow-up and asymptotic stability of weak solutions to the wave equation utt - Δu + |u|kj′(ut) = |u|p-1</sup>u in Ω x (0, T), where p > 1 and j′ denotes the derivative of a C1 convex and real value function j. We prove that every weak solution is asymptotically stability, for every m is such that 0 < m < 1, p < k + m and the initial energy is small; the solutions blow up in finite time, whenever p > k + m and the initial data is positive, but appropriately bounded. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 10 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Hu, Q., & Zhang, H. (2007). Blowup and asymptotic stability of weak solutions to wave equations with nonlinear degenerate damping and source terms. <i>Electronic Journal of Differential Equations, 2007</i>(76), pp. 1-10. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/14272 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University-San Marcos, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.holder | This work is licensed under a Creative Commons Attribution 4.0 International License. | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2007, San Marcos, Texas: Texas State University-San Marcos and University of North Texas. | |
| dc.subject | Wave equation | |
| dc.subject | Degenerate damping and source terms | |
| dc.subject | Asymptotic stability | |
| dc.subject | Blow up of solutions | |
| dc.title | Blowup and asymptotic stability of weak solutions to wave equations with nonlinear degenerate damping and source terms | |
| dc.type | Article |