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Volume 29, Issue 2
A Free Boundary Problem of a Semilinear Combustible System with Higher Dimension and Heterogeneous Environment

Junli Yuan

DOI: 10.4208/jpde.v29.n2.4

J. Part. Diff. Eq., 29 (2016), pp. 124-142.

Published online: 2016-07

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  • Abstract
In this paper, we investigate a free boundary problem of a semilinear combustible system with higher dimension and heterogeneous environment. Such a problem is usually used as a model to describe heat propagation in a two-component combustible mixture in which the free boundary is described by Stefan-like condition. For simplicity, we assume that the environment and solutions are radially symmetric. We use the contraction mapping theorem to prove the local existence and uniqueness of the solution. Also we study the blowup property and the long time behavior of the solution. Our results show that when pq › 1 blowup occurs if the initial datum is large enough and the solution is global and slow, whose decay rate is at most polynomial if the initial value is suitably large, while when p › 1, q › 1 there is a global and fast solution, which decays uniformly at an exponential rate if the initial datum is small.
  • Keywords

Free boundary combustible system blowup global fast solution global slow solution

  • AMS Subject Headings

35K20, 35R35, 92B05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

yuanjunli@ntu.edu.cn (Junli Yuan)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-29-124, author = {Yuan , Junli}, title = {A Free Boundary Problem of a Semilinear Combustible System with Higher Dimension and Heterogeneous Environment}, journal = {Journal of Partial Differential Equations}, year = {2016}, volume = {29}, number = {2}, pages = {124--142}, abstract = { In this paper, we investigate a free boundary problem of a semilinear combustible system with higher dimension and heterogeneous environment. Such a problem is usually used as a model to describe heat propagation in a two-component combustible mixture in which the free boundary is described by Stefan-like condition. For simplicity, we assume that the environment and solutions are radially symmetric. We use the contraction mapping theorem to prove the local existence and uniqueness of the solution. Also we study the blowup property and the long time behavior of the solution. Our results show that when pq › 1 blowup occurs if the initial datum is large enough and the solution is global and slow, whose decay rate is at most polynomial if the initial value is suitably large, while when p › 1, q › 1 there is a global and fast solution, which decays uniformly at an exponential rate if the initial datum is small.}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v29.n2.4}, url = {http://global-sci.org/intro/article_detail/jpde/5084.html} }
TY - JOUR T1 - A Free Boundary Problem of a Semilinear Combustible System with Higher Dimension and Heterogeneous Environment AU - Yuan , Junli JO - Journal of Partial Differential Equations VL - 2 SP - 124 EP - 142 PY - 2016 DA - 2016/07 SN - 29 DO - http://doi.org/10.4208/jpde.v29.n2.4 UR - https://global-sci.org/intro/article_detail/jpde/5084.html KW - Free boundary KW - combustible system KW - blowup KW - global fast solution KW - global slow solution AB - In this paper, we investigate a free boundary problem of a semilinear combustible system with higher dimension and heterogeneous environment. Such a problem is usually used as a model to describe heat propagation in a two-component combustible mixture in which the free boundary is described by Stefan-like condition. For simplicity, we assume that the environment and solutions are radially symmetric. We use the contraction mapping theorem to prove the local existence and uniqueness of the solution. Also we study the blowup property and the long time behavior of the solution. Our results show that when pq › 1 blowup occurs if the initial datum is large enough and the solution is global and slow, whose decay rate is at most polynomial if the initial value is suitably large, while when p › 1, q › 1 there is a global and fast solution, which decays uniformly at an exponential rate if the initial datum is small.
Yuan , Junli. (2016). A Free Boundary Problem of a Semilinear Combustible System with Higher Dimension and Heterogeneous Environment. Journal of Partial Differential Equations. 29 (2). 124-142. doi:10.4208/jpde.v29.n2.4
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