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Published in:
20-10-2019 | Letter to the Editor
On the paper D. Burini, S De Lillo, G. Fioriti, Acta Mech., 229 No. 10 (2018), pp 4215–4228
Published in: Acta Mechanica | Issue 1/2020
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Excerpt
In the paper [1], a free boundary problem on a finite interval depending on time is formulated and solved for a nonlinear diffusion-convection equation. The authors consider:
$$\begin{aligned} \theta _{t}=\theta ^{2}(D\theta _{xx}-\theta _{x}),\;\;\theta= & {} \theta (x,t)\quad t>0, x\in [s_{0}(t),s_{1}(t)], \end{aligned}$$
(1)
$$\begin{aligned} \theta (x,0)= & {} \theta _{0},\;\;x\in [0,L], \end{aligned}$$
(2)
$$\begin{aligned} \theta (s_{0}(t),t)= & {} \alpha ,\;\;t>0, \end{aligned}$$
(3)
$$\begin{aligned} D\theta _{x}(s_{0}(t),t)-\theta (s_{0}(t),t)= & {} -\dot{s_{0}}(t),\;\;t>0, \end{aligned}$$
(4)
$$\begin{aligned} \theta (s_{1}(t),t)= & {} \beta ,\;\;t>0, \end{aligned}$$
(5)
$$\begin{aligned} D\theta _{x}(s_{1}(t),t)-\theta (s_{1}(t),t)= & {} -\dot{s_{1}}(t),\;\;t>0, \end{aligned}$$
(6)
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