Existence of Global Solutions for Systems of Reaction-diffusion Equations on Unbounded Domains
| dc.contributor.author | Badraoui, Salah | |
| dc.date.accessioned | 2020-08-17T20:37:19Z | |
| dc.date.available | 2020-08-17T20:37:19Z | |
| dc.date.issued | 8/19/2002 | |
| dc.description.abstract | We consider, an initial-value problem for the thermal-diffusive combustion system ut = a∆u - uh(v) vt = b∆u + d∆v + uh(v), where a > 0, d > 0, b ≠ 0, x ∈ ℝn, n ≥ 1, with h(v) = vm, m is an even nonnegative integer, and the initial data u0, v0 are bounded uniformly continuous and nonnegative. It is known that by a simple comparison if b = 0, α = 1, d ≤ 1, and h(v) = vm with m ∈ ℕ*, the solutions are uniformly bounded in time. When d > a = 1, b = 0, h(v) = vm with m ∈ ℕ*, Collet and Xin [2] proved the existence of global classical solutions and showed that the L∞ norm of v can not grow faster than 0(log log t) for any space dimension. In our case, no comparison principle seems to apply. Nevertheless using techniques form [2], we essentially prove the existence of global classical solutions if a < d, b < 0, and v0 ≥ b/ a-d u0. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 10 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Badraoui, S. (2002). Existence of global solutions for systems of reaction-diffusion equations on unbounded domains. Electronic Journal of Differential Equations, 2002(74), pp. 1-10. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/12407 | |
| dc.language.iso | en | |
| dc.publisher | Southwest 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, 2002, San Marcos, Texas: Southwest Texas State University and University of North Texas. | |
| dc.subject | Reaction-diffusion systems | |
| dc.subject | Positivity | |
| dc.subject | Global existence | |
| dc.subject | Boundedness | |
| dc.title | Existence of Global Solutions for Systems of Reaction-diffusion Equations on Unbounded Domains | |
| dc.type | Article |