TY - JOUR
T1 - A Free Boundary Problem Arising in Smoulder Combustion
AU - Bei Hu
JO - Journal of Partial Differential Equations
VL - 3
SP - 193
EP - 214
PY - 1994
DA - 1994/07
SN - 7
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5682.html
KW - Free boundary
KW - a priori estimate
KW - variational inequality
KW - asymptotic behavior
AB -  The smouldering combustion is modeled as a free boundary problem here. By using the Duvaut's transform, the problem is reduced to a variational inequality. Existence and uniqueness are established. Tbe properties of the free boundary are studied in various cases. The asymptotic behavior of the free boundary with respect to the parameter is rigorously proved, which confirms the result of a previous work by J. Adler and D. M. Herbert, obtained by using asymptotic expansion. Furthermore, we show that the time dependent problem will actually converge to a travelling wave solution if the boundary data converge to the corresponding travelling wave solution.