## 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