A Free Boundary Problem Arising in Smoulder Combustion

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Volume 7, Issue 3

Bei Hu

J. Part. Diff. Eq.,7(1994),pp.193-214

Published online: 1994-07

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Abstract

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.

Keywords

Free boundary a priori estimate variational inequality asymptotic behavior

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@Article{JPDE-7-193, author = {Bei Hu}, title = {A Free Boundary Problem Arising in Smoulder Combustion}, journal = {Journal of Partial Differential Equations}, year = {1994}, volume = {7}, number = {3}, pages = {193--214}, abstract = { 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.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5682.html} }

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.

Bei Hu. (1970). A Free Boundary Problem Arising in Smoulder Combustion. Journal of Partial Differential Equations. 7 (3). 193-214. doi:

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