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Travelling wave solutions for a drying problem. (English) Zbl 0843.35047

Martin, Gaven (ed.) et al., Proceedings of the miniconference on analysis and applications, held at the University of Queensland, Brisbane, Australia, September 20-23, 1993. Canberra: Australian National University, Centre for Mathematics and its Applications. Proc. Cent. Math. Appl. Aust. Natl. Univ. 33, 107-112 (1994).
A simple model governing the drying of a porous material at a constant wet-bulb temperature is formulated in nondimensional form (with slight modification) as follows: \[ {\partial S\over \partial t}= {\partial\over \partial x} \Biggl\{K_S(S) {\partial S\over \partial x}- K_g(S)\Biggr\},\tag{1} \]
\[ K_S(S)= \begin{cases} \alpha S^3\{f(S)+ {5\over S^2}\},\quad & S> 0,\\ 0,\quad & S\leq 0,\end{cases}\quad K_g(S)= \begin{cases} \beta S^3,\quad & S> 0,\\ 0,\quad & S\leq 0,\end{cases} \] where \(S\) is the moisture content and \(\alpha\) and \(\beta\) are nondimensional constants which are determined by the properties of the porous material and the drying conditions; \(f(S)= \text{const.}+ \text{const.} e^{-40(1- S)}\), these constants being positive. Here, \(x\) is the vertical axis with positive direction downward and \(t\) is time. In this study, we ask whether equation (1) admits travelling plane wave solutions on \(- \infty< x< \infty\).
For the entire collection see [Zbl 0816.00015].

MSC:

35K65 Degenerate parabolic equations
76S05 Flows in porous media; filtration; seepage
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