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Approximation ofa semilinear elliptic problem in an unbounded domain
Published online by Cambridge University Press: 15 March 2003
Abstract
Let f be an odd function of a class C2 such that ƒ(1) = 0,ƒ'(0) < 0,ƒ'(1) > 0 and $x\mapsto f(x)/x$ increases on [0,1]. We approximate the positive solution of Δu + ƒ(u) = 0, on $ \xR_{+}^{2}$ with homogeneous Dirichlet boundary conditions by the solution of $-\Delta u_{L}+f(u_{L})=0,$ on ]0,L[2 with adequate non-homogeneous Dirichlet conditions. We show that the error uL - u tends to zero exponentially fast, in the uniform norm.
- Type
- Research Article
- Information
- ESAIM: Mathematical Modelling and Numerical Analysis , Volume 37 , Issue 1 , January 2003 , pp. 117 - 132
- Copyright
- © EDP Sciences, SMAI, 2003
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