Reiner Schätzle

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We consider the spatially inhomogeneous and anisotropic reaction-diffusion equation u t = m(x) −1 div[m(x)a p (x, ∇u)] + ε −2 f (u), involving a small parameter ε > 0 and a bistable nonlinear term whose stable equilibria are 0 and 1. We use a Finsler metric related to the anisotropic diffusion term and work in relative geometry. We prove a weak comparison(More)
(i) The two-phase Stefan problem (1) @tu ? Duxx = 0 for 0<x<s(t) ; @tu ? uxx = 0 for s(t) < x < 1 ; u(s(t); t) = 0 ; ux(0; t) = ux(1; t) = 0 ; s 0 (t) = ux(s(t)+; t) ? Dux(s(t)?; t) ; where fx = s(t)g is the moving boundary, models the melting and solidiication of materials. It is interesting both from the engineering and the numerical points of view to be(More)
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