Abstract
As mentioned earlier, when the reaction term in (1.1) is absent and the partial differential equation is
the integral equation (1.9) reduces to the simple identity θ(s) = σs+b(s) . Subsequently, if this ‘equation’ is to have a nonnegative solution on [0,ℓ] with ℓ < ∞ such that θ(ℓ)= 0, then necessarily σ = -b (ℓ) / ℓ and θ (s)= b (s) — sb (ℓ) / ℓ ≥ 0 for all 0 ≤ s ≤ℓ . By Lemma 2.40 though θ satisfies the integrability condition if and only if it is positive on (0, ℓ). We conclude the following.
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© 2004 Springer Basel AG
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Gilding, B.H., Kersner, R. (2004). Wavefronts for convection-diffusion. In: Gilding, B.H., Kersner, R. (eds) Travelling Waves in Nonlinear Diffusion-Convection Reaction. Progress in Nonlinear Differential Equations and Their Applications, vol 60. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7964-4_9
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DOI: https://doi.org/10.1007/978-3-0348-7964-4_9
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9638-2
Online ISBN: 978-3-0348-7964-4
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