On The Method of Lower and Upper Solutions for the Heat Equation on a Polygonal Domain
| dc.contributor.advisor | Abdi Tadesse (PhD) | |
| dc.contributor.author | Sahile Tesfaye | |
| dc.date.accessioned | 2018-07-19T06:05:56Z | |
| dc.date.accessioned | 2023-11-04T12:30:39Z | |
| dc.date.available | 2018-07-19T06:05:56Z | |
| dc.date.available | 2023-11-04T12:30:39Z | |
| dc.date.issued | 2016-07 | |
| dc.description.abstract | The purpose of this paper is to prove the existence of a solution in the presence of lower and upper solutions for the nonlinear periodic-Dirichlet heat equation on a polygonal domain Ω of the plane in weighted Lp-Sobolev spaces. Consider the problem; ∂tu − Δu = f(x, t, u), in Ω × (−π, π), u = 0, on ∂Ω × (−π, π), u(•,−π) = u(•, π) in Ω, loc (Ω)}, with a real parameter μ and r(x) the distance from x to the set of corners of Ω. We prove some existence results of this problem in presence of lower and upper solutions well-ordered or not. We first give existence results in an abstract setting obtained using degree theory. We secondly apply them for polygonal domains of the plane under geometrical constraints | en_US |
| dc.identifier.uri | http://etd.aau.edu.et/handle/123456789/9303 | |
| dc.language.iso | en | en_US |
| dc.publisher | Addis Ababa University | en_US |
| dc.subject | Method of Lower and Upper Solutions | en_US |
| dc.title | On The Method of Lower and Upper Solutions for the Heat Equation on a Polygonal Domain | en_US |
| dc.type | Thesis | en_US |