1 results
Approximation ofa semilinear elliptic problemin an unbounded domain
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- Journal:
- ESAIM: Mathematical Modelling and Numerical Analysis / Volume 37 / Issue 1 / January 2003
- Published online by Cambridge University Press:
- 15 March 2003, pp. 117-132
- Print publication:
- January 2003
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- Article
- Export citation
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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 thesolution of $-\Delta u_{L}+f(u_{L})=0,$ 
on ]0,L[2 with adequatenon-homogeneous Dirichlet conditions. We show that the error uL - utends to zero exponentially fast, in the uniform norm.
