Browsing by Author "Sahile Tesfaye"

Now showing 1 - 1 of 1
  • No Thumbnail Available
    Item
    On The Method of Lower and Upper Solutions for the Heat Equation on a Polygonal Domain
    (Addis Ababa University, 2016-07) Sahile Tesfaye; Abdi Tadesse (PhD)
    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