Blow-up for parabolic equations in nonlinear divergence form with time-dependent coefficients
| dc.contributor.author | Shen, Xuhui | |
| dc.contributor.author | Ding, Juntang | |
| dc.date.accessioned | 2023-03-30T17:57:11Z | |
| dc.date.available | 2023-03-30T17:57:11Z | |
| dc.date.issued | 2022-01-25 | |
| dc.description.abstract | In this article, we study the blow-up of solutions to the nonlinear parabolic equation in divergence form, (h(u))t = n∑i,j=1 (ɑ ij(x)uxi)xj - k(t)ƒ(u) in Ω x (0, t*), n∑i,j=1 ɑ ij(x)uxi vj = g(u) on ∂Ω x (0, t*), u(x, 0) = u0(x) ≥ 0 in Ω̅, where Ω is a bounded convex domain in ℝn (n ≥ 2) with smooth boundary ∂Ω. By constructing suitable auxiliary functions and using a differential inequality technique, when Ω ⊂ ℝn (n ≥ 2), we establish conditions for the solution blow up at a finite time, and conditions for the solution to exist for all time. Also, we find an upper bound for the blow-up time. In addition, when Ω ⊂ ℝn with (n ≥ 3), we use a Sobolev inequality to obtain a lower bound for the blow-up time. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 17 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Shen, X., & Ding, J. (2022). Blow-up for parabolic equations in nonlinear divergence form with time-dependent coefficients. <i>Electronic Journal of Differential Equations, 2022</i>(08), pp. 1-17. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/16512 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2022, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Nonlinear parabolic equation | |
| dc.subject | Blow-up | |
| dc.subject | Upper bound | |
| dc.subject | Lower bound | |
| dc.title | Blow-up for parabolic equations in nonlinear divergence form with time-dependent coefficients | |
| dc.type | Article |